Identification of geomorphological dynamics
from bathymetric time series acquired by radar
(Vom Coastal Research Laboratory, Forschungs- und Technologiezentrum
Westküste BÜSUM, der Christian-Albrechts-Universität zu Kiel als Diplomarbeit angenommen)
Author:
ISSN 0344-9629
N. Alamsyah
GKSS 2008/9
GKSS 2008/9
Identification of geomorphological dynamics
from bathymetric time series acquired by radar
(Vom Coastal Research Laboratory, Forschungs- und Technologiezentrum
Westküste BÜSUM, der Christian-Albrechts-Universität zu Kiel als Diplomarbeit angenommen)
Author:
N. Alamsyah
(Institute of Coastal Research)
GKSS-Forschungszentrum Geesthacht GmbH • Geesthacht • 2008
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GKSS 2008/9
Identification of geomorphological dynamics from bathymetric time series acquired by radar
(Vom Coastal Research Laboratory, Forschungs- und Technologiezentrum Westküste BÜSUM, der ChristianAlbrechts-Universität zu Kiel als Diplomarbeit angenommen)
Novrizal Alamsyah
117 pages with 34 figures and 2 tables
Abstract
The remote sensing techniques are being used for monitoring the phenomena at the coastal
region. The nautical X-band Radar which is mounted in the List West of Sylt by the Department
of Radar Hydrography of GKSS Research Centre is used to determine important hydrographic
parameter and the water depth. In this thesis, the theoretical accuracy of the Dispersive Surface
Classificator (DiSC) used for the analysis of ground based X-band radar image sequences is estimated by the chi-squared distribution to construct the confidence limit of variance. The analyzed
data are used for the identification of the tidal cycle and the monitoring of the impact of a severe
storm as well the summer period effect on the sediment bedforms. The inversion of local wave
in space and time proved that the in situ gauge can be simulated. The comparison between DiSC
and tidal gauge water level has a significant correlation (corr = 0.77) at the selection area
(81 neighboring cells). The morphodynamic evolution of the ship channel in Lister Tief is also
examined. The long term comparison, February to October 2002, has proved that in the area of
investigation, there are dynamic but stabilized sediment structures. Generally, it is proven that
the characteristic of the channel (slope, absolute depth, width) have great variability and strong
dependencies to short period, severe phenomena, such as a storm and to the seasonal impact of
the normal, tidal water circulation. Both effects are important for the monitoring of the coastal
evolution and protection. Finally, the ground based X-band radar could be characterized as a
method for the operational monitoring of the coastal zone.
Identifikation von morphodynamischen Prozessen aus bathymetrischen Zeitserien mittels
landgestützten Radars
Zusammenfassung
Fernerkundungstechniken werden unter anderem benutzt, um physikalishe Phänomene der
Küstenregionen zu beobachten. Das nautische X-band-Radar, welches auf der Nordseeinsel
Sylt, nahe dem Leuchtturm List West, installiert ist, wird von der Abteilung Radarhydrographie
des GKSS-Forschungzentrums dazu verwendet, wichtige, hydrographische Parameter, wie die
lokale Wassertiefe, zu erfassen. In dieser Arbeit wird die theoretische Genauigkeit der Dispersive
Surface Classificator(DiSC)-Software zur Analyse von landbasierten Radarsequenzen durch
Chi-squared-Verteilung abgeschätzt, um einen glaubwürdigen Toleranzgrenzwert zu erzeugen.
Die analysierten Daten werden dazu benutzt, um einen Tidezyklus zu identifizieren, den Einfluss
von Sturmereignissen zu überwachen und ebenso den Effekt auf den Meeresboden während des
Sommers zu beobachten. Die Invertierung der lokalen Wellen in Raum und Zeit beweist, dass
In situ-Messungen simuliert werden können. Ein Vergleich zwischen DiSC- und Tide-Pegelwerten
zeigt einen signifikanten Zusammenhang (corr = 0.77) im ausgewählten Gebiet (81 benachbarte
Zellen). Die morphodynamische Entwicklung des Tidekanals Lister Tief wurde ebenfalls untersucht. Ein Langzeitvergleich von Februar bis Oktober 2002 hat bewiesen, dass im beobachteten
Gebiet dynamische aber stabile Sedimentstrukturen existieren. Im Allgemeinen wurde bewiesen,
dass die hydrodynamischen Charakteristika des Lister Tiefs (Gefälle, Wassertiefen, Breite) hoch
variable und stark abhängig von Phänomenen mit kurzer Periode, wie Stürmen und dem saisonalen
Einfluss der normalen Tidezirkulation, sind. Beide Effekte sind wichtige Parameter bei der
Überwachung der Küstenentwicklung und des Küstenschutzes. Abschließend kann gesagt werden,
dass das landgestützte X-band-Radar eine Methode ist, um eine operationelle Überwachung der
Küstenregion zu gewährleisten.
Manuscript received / Manuskripteingang in TKP: 20. August 2008
Table of Contents
Table of Contents
Table of Contents....................................................................................................................I
Tables and Figures ............................................................................................................... III
Acknowledgement ...............................................................................................................IX
Notations............................................................................................................................... X
1
Introduction....................................................................................................................1
1.1
Objective.......................................................................................................................1
1.2
Background ...................................................................................................................2
1.3
Outline ..........................................................................................................................4
2
Literature Review ..........................................................................................................5
2.1
The Study Area ............................................................................................................. 5
2.2 Water Level Measurement and The Importance of Remote sensing............................7
2.
Erosion and Deposition…………………………………….......................................10
3
Theoritical Background ...............................................................................................12
3.1
Microwave Radar Remote Sensing Applied in Oceanography .................................14
3.1.1
Radar Equation ............................................................................................15
3.1.2
Sea Clutter....................................................................................................16
3.1.2.1 Back scatter Mechanisms………………………………………..18
3.1.2.2
3.1.3
Bragg Backscattering…………………………………………….18
Modulation Mechanisms..............................................................................20
3.1.3.1
Tilt………………………………………………………………..21
3.1.3.2
Hydrodynamic…………………………………………………...21
3.1.3.3
Shadowing……………………………………………………….21
3.2 Sea Surface Waves….…………………………...……………………………………22
3.2.1
Linear Wave Theory ....................................................................................23
3.2.2
Stationarity of Wave Field...........................................................................25
3.2.3
Homogeneity Wave Field………………………………………………….25
3.2.4
Dispersion Relation………………………………………………………..26
3.2.5
Water Depth and Near Surface Current…………………………………...29
3.3 Dispersive Surface Clasificator……………………………………………………...30
Coastal Geosciences and Engineering, University of Kiel
I
Table of contents
4
4.1
4.2
3.3.1
Assumption of DiSC............................................................................... 31
3.3.2
Input Parameter....................................................................................... 32
3.3.3
The Algorithm of DiSC .......................................................................... 32
Methodology............................................................................................................... 35
Data Selection........................................................................................................... 35
4.1.1
Experimental Setup: Sylt ......................................................................... 35
4.1.2
Wind Data................................................................................................ 35
4.1.3
Radar Data.........................................................................................…...36
Data Processing ........................................................................................................ 37
4.2.1
Export of data ........................................................................................... 39
4.2.2
Identification of the Tidal Signal.............................................................. 39
4.2.2.1 Confidence Interval of Variance……………………………… 40
4.2.3
The Regression Analysis of Water Level……………………………….41
4.2.4
The Time Lag Analysis between List Westerland and List Tief………..42
4.2.5
Visualization Average Bathymetry Map………………………………..43
4.2.6
Defining Cross Section…………………………………………………43
4.2.6.1
Depth Analysis over Cross Section………………………...43
4.2.6.2
Slope Analysis over Cross Section…………………………44
5
Results ......................................................................................................................... 45
6
Discussion.................................................................................................................... 53
7
Conclusions ................................................................................................................. 57
References............................................................................................................................59
Appendices...........................................................................................................................A1
II
Coastal Geosciences and Engineering, University of Kiel
Table and Figure
Tables and Figures
Figure 2.1 Maps for the localization of the area research position, in the black frame
on the right map, (FLAMPOURIS 2007).....................................................................7
Figure 3.1: Scheme to visualize the relation between scattering wave with the length
λs and the electronic wave with the length λr. The relation between those two is observed by (ESA, 1956) and consist the basic principle of the radar system...............................................................................................................................20
Figure 3.2: Classification of ocean waves and their relative energy..........................23
Figure 3.3: A simple sinusoidal wave.........................................................................23
Figure 3.4: Sea-surface obtained from the sum of many sinusoidal waves (derived
from Pierson et al. 1995).............................................................................................24
Figure 3.5: spectral instationarity and inhomogeneity illustrated in a 2D k-ω section.
(SENET 2004)............................................................................................................26
Figure 3.6: Positive and negative dispersion relation of linear deep-water surfacegravity waves in 3DΩ domain, (SENET 2004)..........................................................28
Figure 3.7: Dispersion relation of linear surface-gravity waves in 3D Ω domain: a)
intrinsic deep-water dispersion shell, b) intrinsic shallow water dispersion shell and
c) Doppler shifted deep-water dispersion shell influenced by near-surface current,
(SENET 2004)............................................................................................................29
Coastal Geosciences and Engineering, University of Kiel
III
Table and Figure
Figure 3.8 Scheme of the procedural and data flow of DiSC (FLAMPOURIS
2007)...........................................................................................................................31
Figure 3.9: Spectral decomposition by filtering (SENET 2004)................................33
Figure 4.1 Flow chart of data processing consist 2 procedure, procedure 1 as the investigation of theoretical accuracy of DiSC and procedure 2 as the observation of
morphodynamic changes............................................................................................38
Figure 5.1: Graph representing the tidal cycle during period 1 at 26th-27th February
2002 after subtracting the mean water level of the series from every time step. The
pink line is tidal gauge measurement in Westerland and the blue line is the estimated
tidal cycle from radar sequences. The bars show confidence interval of variance.
a.the average radar water level at the 81 neighboring cells around the point
(3460944.34, 6103240.84); b. the average radar water level after filtering with ± 0.25
m at the 81 neighboring cells......................................................................................46
Figure 5.2: Graph representing the tidal cycle during the period 2 at 7th March 2002
after subtracting the mean water level of the series from every time step. The pink
line is tidal gauge measurement in Westerland and the blue line is the estimated tidal
cycle from radar sequences. The bars show confidence interval of variance. a. the
average radar water level at the 81 neighboring cells around the point (3460944.34,
6103240.84); b. the average radar water level after filtering with ± 0.25 m at the 81
neighboring cells.........................................................................................................47
Figure 5.3: The correlation coefficient produced by comparison between gauge water
level and radar water level at 81 neighboring cells, and homogenous
area..............................................................................................................................48
Figure 5.4: Cross correlation analysis between water level in List Tief (radar deduced) and water level in List-Westerland (gauge deduced) with the same local time.
The blue bars show the cross correlation coefficient for both water levels. a. cross
IV
Coastal Geosciences and Engineering, University of Kiel
Table and Figure
correlation at 26th-27th February 2002); b. cross correlation at 07th March
2002.............................................................................................................................49
Figure 5.5: Depth of the area of investigation during the storm period (26th-27th February 2002), as a result of averaging the calculated depths for 12 hours. The R symbol is the radar position. The white dot is the cross section A-B and CD.................................................................................................................................50
Figure 5.6: The comparison of depth at the cross section A-B during the three difference periods; the reference is defined as the average of water level in
2002……………………………………………………………………………….....51
Figure 5.7: The comparison of the slope over the cross section (A to B) for the three
different periods..........................................................................................................51
Table 3.1: Properties of the X-Band Furuno 1201 nautical radar (ANONYMOUS
1989)...........................................................................................................................15
Table 4.1 Specification of the Cartesian grid of the ground based nautical radar images sequences.............................................................................................................37
Figure I-1: Sand nourishment at Sylt (GENERALPLAN KUSTENSCHUTZ).........A1
Figure II-1: Plot wind speed and water level at the period 1 (27 February 2002)......A2
Figure II-2: Plot wind speed and water level at the period 2 (7 March 2002)............A2
Figure II-3: Plot wind speed and water level at the period 3 (28 October 2002)........A3
Figure III-1: Plot wind direction and water level at the period 1 (26-27 February
2002)..........................................................................................................................A4
Coastal Geosciences and Engineering, University of Kiel
V
Table and Figure
Figure III-2: Plot wind direction and water level at the period 2 (7 March 2002).....A4
Figure III-2: Plot wind speed and water level at the period 3 (28 October 2002).....A5
Figure V-1: Plot of upper limit, lower limit (
ν
ν
,
) vs. ν for
χν (α / 2) χν (1 − α / 2)
(1 − α ) = 0.80, 0.95, 0.99 (derived from JENKINS and WATTSS (1968), “Spectral
Analysis and its Application”).................................................................................A19
Figure V-2: Table of Chi-Squared (derived from Newbold (1984), “Statistics for
Business and Economics”).......................................................................................A20
Figure VI-1: Graph representing the tidal cycle during period 3 at 28 October 2002
after subtracting the mean water level of the series from every time step. The pink
line is tidal gauge measurement in Westerland and the blue line is the estimated tidal
cycle from radar sequences. The bars show confidence interval of variance. a. the
average radar water level at the 81 neighboring cells around the point (3460944.34,
6103240.84); b. the average radar water level after filtering with ± 0.25 m at the 81
neighboring cells......................................................................................................A21
Figure VII-2: Atmospheric pressure (barometric phenomena) (FLAMPOURIS 2008),
Sylt is denoted with black arrow..............................................................................A22
Figure VIII-1: Depth of the area of investigation during the storm period 2 (7 March
2002), as a result of averaging the calculated depths for 12 hours. The R symbol is
the radar position. The white dot is the cross section A-B and C-D........................A23
Figure VIII-2: Depth of the area of investigation during the storm period 3 (28 October 2002), as a result of averaging the calculated depths for 12 hours. The R symbol
is the radar position. The white dot is the cross section A-B and C-D………........A24
VI
Coastal Geosciences and Engineering, University of Kiel
Table and Figure
Figure IX-1: Visualization of hourly bathymetries of one tidal cycle, during period 2
(7th March 2002)......................................................................................................A30
Figure X-1: The comparison of depth at the cross section C-D during the three difference periods; the reference is defined as the average of water level in
2002..........................................................................................................................A31
Figure X-2: The comparison of the slope over the cross section (C to D) for the three
different periods ......................................................................................................A31
Coastal Geosciences and Engineering, University of Kiel
VII
Table and Figure
VIII
Coastal Geosciences and Engineering, University of Kiel
Acknowledgements
Acknowledgements
First of all, I would like to thank my supervisor Dr. F. Ziemer for giving me the
opportunity to work at the Department of Radar Hydrography (KOR) of GKSS
Center. This thesis would not have been possible without kind support, the critiques,
the probing questions, and the remarkable patience from him. I am also truly and
deeply thankful to Professor R. Mayerle, Director of the Master Course Coastal
Geosciences and Engineering, University of Kiel for permitting me to pursue my
thesis at GKSS and contribute as supervisor.
I am also very grateful to S. Flampouris, PhD student at KOR, for giving me
guidance, and helping me to find solutions for my problem. His ability to explain
scientific makes my life easier to writing thesis. I also want to thank M. Cycewski
and S. Sedlacek, for tutoring me in PV-Wave programming and their help in
practical problem. I also want to acknowledge G. Schymura for providing
measurement data.
Finally, I would like my special thanks for my parents who always giving me totally
support in my whole life. I also can’t forget Mirna Sophia who always gives me
encouragement to do my best in all matter in my life.
Coastal Geosciences and Engineering, University of Kiel
IX
Notations
Notations
ı2
variance
μ
mean
w
G
k
G
r
G
uc
partial derivation operator
CG
group velocity of sea-surface waves (ms-1, ms-1)
Cp
phase velocity of a sea-surface wave (ms-1, ms-1)
d
water depth (m)
f
frequency (s-1)
Ȧ
circular frequency (s-1)
g
gravitational acceleration
k
wavenumber (rad m-1), magnitude
kx , k y , kz
Cartesian wavenumber components (rad m-1)
t
time (s)
x,y,z
spatial coordinates (m)
Ĭ
3D spatio-temporal domain (m, m, s)
ȍ
3D wavenumber-frequency domain (rad m-1, rad m-1 rad s-1)
Ȝ
wavelength (m)
ș
incidence angle
IJ
waveperiod
ȗ
sea-surface elevation (m)
Ȣ
intrinsic dispersion of sea-surface waves (rad s-1)
Ȣ+, Ȣ -
positive and negative solution of dispersion (rad s-1)
Pr
received signal power
Pt
power
Gt
gain
R
distance
Ae
effective aperture area
Os
scattering wave length
Or
electromagnetic wave
X
2D wavenumber vector of sea-surface waves (rad m-1, rad m-1)
spatial vector
2D near-surface current vector (ms-1, ms-1)
Coastal Geosciences and Engineering, University of Kiel
1. Introduction
1.
Introduction
The coastal zone plays an important role to the welfare of human and economy
which are inextricably linked to the features and activities that occur within this
dynamic region. More than 44 % of the world population lives within 150 km of the
coast. In 2001 over half the world population lived within 200 km of a coastline
(UNEP 2006). The spatial and temporal variations of coast on all scales affect lives
and environment significantly. As the coastal communities grow, the pressure of the
environment is increasing due to the human activities such as economical and
recreation activities. Therefore, the monitoring of oceanographic phenomena, the
protection and the development of the coastal zone of socio-economical interest are
required.
The knowledge of the bathymetry is one of the most important factors for coastal and
marine activity because the changes of the bathymetry have direct influence on the
human activities. The attainment of spatial and temporal bathymetries is part of the
oceanographic routine; the methods are from rope and plummet to sonar and echo
sounding and nowadays by the development of the remote sensing and concrete
wave theory, since the first trips of exploration the bathymetric data is a requirement
(FLAMPOURIS 2006). Thus long term monitoring using a variety of coastal
monitoring systems is needed to better understand coastal phenomena and assess the
sustainability of the coasts.
1.1 Objective
The main focus of the investigation is the application of ground based X-band radar
on determination of water level and bathymetry.
The objectives of this study are:
1. Identification of the tidal signal at the DiSC results by integrating tide
gauge measurement and wind influence.
2. Accuracy of the method and the application of DiSC results as virtual
tidal gauge.
Coastal Geosciences and Engineering, University of Kiel
1
1. Introduction
3. Comparison of depth and slope over two cross sections to identify the
morphodynamic changes in the area of investigation.
The long-term goals are the improvement of DiSC system as oceanographic
instrument and operational system for the bathymetric monitoring of coastal regions.
1.2 Background
The sea state and the tidal currents act as forces which induce morphodynamic
changes in coastal waters and on the coastline. The knowledge of the bathymetry, at
the near shore area and over various spatial and temporal scales, is important for
understanding such an interactive regime. Traditional surveying methods of
qualifying the depth are inherent labor intensive as they involve manual deployment
of expensive instrument over the area of interest. Even with sophisticated depth
measuring device like sonar altimeters and global positioning satellite units, the
process remains costly in terms of both time and money. Satellite till now are not
applicable in coastal area. It is not feasible to use these methods to cover large spatial
distance (MISRA, KENNEDY, and KIRBY 2001). Therefore, there is urgent need
for a cost-effective remote sensing method, which allows the retrieval of the geo
dynamics.
For the last three decades, the RADAR (RAdio Detecting And Ranging) remote
sensing is flourished. The first civil system was the CODAR of NOAA (BARRICK
1977), a high frequency system which concerns mainly the measurement of ocean
wave and currents. Since the first system of CODAR then there are several projects
around the world based on spatial and temporal structure analysis of radar images of
the sea surface. The algorithm have been evolved to measure the wave direction
spectra within a 2 km2 patch of the sea using a nautical radar which permit to provide
sea state parameters such as significant wave height and peak period. At least two
companies commercialized this radar system, the Wave Monitoring System
(WaMoS), developed by GKSS research center in Germany (ZIEMER 1991 & 1995,
ZIEMER & DITTMER 1994 and NIETO BORGE 1999) and the Marine Radar
Wave Extraction (WAVEX), developed by the MIROS AS company in Norway
(GRONLIE, 1995 and GANGESKAR & GRONLIE 2000).
2
Coastal Geosciences and Engineering, University of Kiel
1. Introduction
The microwave remote sensing method such as ground based X-band radar is
suitable for monitoring the waves in coastal zone, with the wave field ranging from
few meters to few hundred meters. Therefore, the ground based X-band radar is the
adopted wave and current measurement tool. The advantage of deployment nautical
X-band radar systems can typically be made in severe storm without high risk of
damage the instrument. Nautical X-band radar is not impeded by most weather or
light conditions. The only exception is heavy rainfall that increases the background
noise in a way that no “signal” is detectable.
For the implementation of the objective, the input data are retrieved by using a
remote sensing method (X-band radar) and the Dispersive Surface Classificator
(DiSC) software. From the acquired image sequences, hydrographic parameters, such
as the water depth (OUTZEN 1998, WOLFF et al.1999) are determined. DiSC is an
algorithm that analyses image sequences for the determination of the physical
parameters on a local spatial scale, it consist a local analysis method, which allow the
analysis of inhomogeneous image sequences of a dynamic and dispersive surface.
The method used to date, used the noise to signal ratio, are based on the analysis of
radar backscatter signal variance spectra calculated by modulus of a 3D Fast Fourier
Transformation (3D FFT) performed on the image sequences. The waves phase maps
are estimated and inversed in local scale for the determination of the bathymetry.
The raw radar data were acquired by X-band radar which was mounted at the island
Sylt Isle close to the lighthouse List West, a coastal area with high morphodynamical
activity, as there is a sand bar which could change the impact
hydrodynamic
effectively. The radar data is mounted from the 2001 until 2007 with gaps in data
acquisition. For the same period, there are available wave buoy data (GKSS), water
level data (ALR) and wind data acquired at the radar position. As the DiSC method
is applicable during storm period, the available meteorological data have been
analyzed and according to them the analysis period of the thesis have been chosen.
The thesis is focused on the investigation of the bathymetric surveys during three
different periods in 2002. The occurred bathymetries constitute a time series every
0.5h with a total of 24 steps (one period) and 1h with total 12 steps (two periods)
each one tidal cycle.
Coastal Geosciences and Engineering, University of Kiel
3
1. Introduction
1.3 Outline
The thesis is consisted by seventh chapters. In the first chapter the introduction is
described the background of thesis. In the second chapter the study is described the
literature on which the thesis based reviewed. The third chapter describes the
principles of the mechanism of radar to determine the wave field characteristics and
the DiSC (Dispersive Surface Clasificator). In the fourth chapter, the methodology of
the thesis is presented. The achievements procedure by the thesis are presented in
chapter fifth to seventh where the results are illustrated, discussed and the initial
queries are fulfilled.
4
Coastal Geosciences and Engineering, University of Kiel
2. Literature Review
2. Literature Review
2.1 The Study Area
The island of Sylt is the northernmost outpost in Germany and sits on the West coast
of Schleswig-Holstein at North Sea coast of German Bight. Sylt has a length 35 km
from north to south and a width up to 13 km from east to west, its surface is 99 km2.
The length of the sandy coastline in North-South direction is about 40 km. The
narrowest point of the island is less than 400 m wide. The island was once part of the
mainland, and is still shrinking owing to erosion due to the sea state, which is
common for most islands and shorelines in the region, which are slowly but
constantly changing.
The tide in area of Sylt is semi-diurnal with a maximum tidal heave of approximately
2 m, which cause cross shore transport through the gaps between barier island of
German Bight. The longshore transport along the coast is overlaid by wave impact
and also alternates in direction, which is obvious at the shape Sylt. The island grows
northward as well as southward by spit prolongation in both directions. The
nearshore area is characterized by a longshore bar, which is located approximately
300 m seaward of the shoreline. During storm surges, with a water level rise of more
than 2 m, the protective effect of the bar (crest height approximately 3 m) is lost and
waves pass over the bar without breaking. According to geological estimates, the
west coast of Sylt has receded approximately 13 km over a period of 7000 years (1.8
m/year). Since monitoring started (1870) the recession rate has been 0.9 m/year.
Over this period, the underwater profile has been shifted eastwards, probably without
much change in shape. The eroded material has created spits to the north and south
of the centre of the island. These are now curtailed by major tidal channels. Tidal
currents carry the sand that arrives at the ends of the spits away from the island.
Thus, Sylt is a typical example of an open sand system, because eroded material is
not returned to the island (HAMM 2002).
Attempts since 1865 to slow down dune recession by various types of groins along
large parts of the island have been fairly unsuccessful, as was a seawall (built in
1907) in the middle of the island (Westerland), which needed gradual reinforcement
Coastal Geosciences and Engineering, University of Kiel
5
2. Literature Review
and extension. Since 1972, repeated beach nourishments have been carried out
regularly to protect this seawall and its 3 km-long revetment against under scouring.
Since 1950, greater storm surge frequency has caused the mean yearly recession rate
to increase from 0.9 m/year (1870–1950) to 1.5 m/year (1950–1985), which is
equivalent to an annual loss of 1.5 million m3 of sand (1/3 to the south and 2/3 to the
north). This prompted the coastal authorities (‘Amt für Ländliche Räume’ in Husum)
to initiate a specific coastal protection master plan in 1985, for a period of 35 years
(1985–2020), which has recently been updated in 1997. This assumed that the
increased storm surge frequency would continue, and with it, the erosion that would
endanger the island if no counter-measures was undertaken. All possible alternatives
for future coastal protection of the west coast were considered, and their technical,
economic and environmental aspects indicated that repeated replenishments in the
form of deposits on the beach and shoreface nourishments would provide the most
favorable solution. In the updated nourishment concept, it is intended to maintain the
coastline in its 1992 position by compensating for the mean yearly sand loss from the
coast. The coastline is defined by the dune foot (3.75 m above mean sea level). The
order in which various areas have to be nourished is determined by the degree to
which the sites along the west coast are endangered (NEWE & DETTE 1995).
The vulnerable island Sylt has a multi-functional socio-economic nature and is
covered by a mixture of natural and cultural land uses. Besides high-level standards
in living and recreation facilities, Sylt offers unique aspects of a biotope. The area of
Sylt consists of national park which is strongly bounded with the ecological
environment of Wadden Sea.
The urge of protecting the coastal area at Sylt is a major concern due to the activities
within the area. Extensive work had been done for preventing it, since the 1960’s
effort for protecting was started then it took place intensely at 1980’s (APPENDIX
I), one of method is sustainable monitoring system. Therefore, the sufficient
continuous and accurate data are necessitated for anticipating the problems which
will be occurred in Sylt. The significant role of radar Hydrography is to observe and
acquire data for systematic assessment of sediment movement with any weather
circumstances.
6
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Figure 2.1 Maps for the localization of the area research position, in the black frame on the
right map, (FLAMPOURIS 2007).
2.2 Water Level Measurement and the Importance of
Remote Sensing
Remote sensing techniques as indirect observation method have great capabilities for
monitoring sea state such as water level monitoring. Water level monitoring over
long periods of time are particularly helpful in understanding the circulation of the
ocean. The measurement of sea level stands out as one of the simplest and most
effective methods for establishing long-term global databases of ocean observations.
Bathymetry in the nearshore changes continuously under energetic interactions with
shoaling and breaking waves. In the dynamically active coastal area, the bed
topography change due to an active interaction between sediment transport and
hydrodynamic processes. An accurate knowledge of the ocean floor, particularly in
the nearshore region over spatial and temporal scale, is very important in
understanding such as interactive regime (MISRA, KENNEDY, and KIRBY, 2002).
Nearshore bathymetry is required to describe depth-induced wave changes and largescale fluid motions (YOO 2007). Changes in bathymetry can occur on time scales as
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short as hours due to the presence of large storms. Data are especially difficult to
collect during periods of large waves or strong currents. However, these conditions
often represent the most energetic periods for hydrodynamics, morphodynamics, and
are the times of greatest scientific interest (HASAN & TAKEWAKA 2007).
The in-situ instruments can record the variation of water surface elevations,
velocities, sediment concentration, bottom elevation etc. These instruments are a
powerful tool for monitoring nearshore regions. However, the measurements are
expensive and limited in spatial extent. Further, during energetic sea states it is not
easy to maintain data collection. Remote sensing techniques provide a feasible
alternative due to they allow sampling over large spatial extents (meters to
kilometers) and temporal scales (seconds to years).
The one of earliest forms of remote sensing is aerial photography which used to
image wave field. The utilized of wave-shoaling photographic imagery and the
observed reduction of ocean wave phase speed with decreased water depth was used
as early as World War II to provide useful estimates of bathymetry in coastal
environment (TRIZNA 2001). Nowadays, video camera and radar are becoming
popular for continuous monitoring. Video cameras can monitor the sea surface
patterns with high temporal resolution typically several images per second. However,
the spatial coverage is limited with single camera, which necessitates multiple
cameras in order to gain wide coverage. One severe shortcoming is that the use of
video cameras is limited to daylight hours and fair atmospheric conditions.
The estimation of hydrodynamic and morphodynamic parameters from video images
is just one of a suite of recent techniques. Stockdon and Holman (2000) developed an
advanced method to estimate nearshore bathymetry based on video processing. They
calculated wavenumber components from the gradient of the wave phase propagation
of the dominant incidental band, and a linear dispersion relationship was used to
estimate water depths. A similar analysis has been used by Holland (2001) for time
series data from bottom mounted pressure sensors. He found that the inclusion of
finite amplitude effects in the linear dispersion relationship improved his depth
predictions. Piotrowski and Dugan (2002) used a sequence of video images of
shoaling ocean waves to retrieve maps of water depth and currents. Some other
studies also used inversion techniques to retrieve bathymetry.
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Some of the limitation of video imaging can be overcome by using X-band radar.
The pixel intensity of the radar image corresponds to the relative amount of
backscatter signal from sea surface of the emitted radar beam, which allows its use
during night and under slightly rainy and storm conditions as well. Radar image
sequences with high spatial resolution and large coverage offer a unique opportunity
to study individual waves and wave field in space and time.
Nowadays, the use of X-band radars in coastal studies is becoming popular. Young et
al. (1985) first described an approach using three-dimension Fourier transform
analysis on a sequence of radar images. The resulting wave number spectra were
inverted to frequency spectra with information the water depth. Izquierdo et al.
(2005) compared the ocean wave field derived from X-band radar and wave-rider
buoy measurements by spectral analysis. The comparison show a good agreement
between variations of significant wave height, peak frequency and mean period
obtained from both devises. The estimated directional spectra from their radar
observations were broad banded due to coexistence of storm generated swell and
wind wave. Bell (1999, 2001) succeeded in determining near-shore bathymetry after
analyzing X-band radar images. He applied a linear depth inversion technique,
considering peak period of Fast Fourier Transformation (FFT), and wave celerity
from cross correlation between sequences of images. Bell et al. (2004) used two
different type of radar (X-band and MMW radar) to infer water depth and tried to
improve further the depth inversion. Hessner et al. (1999b) have discussed the use of
space-time behavior of the sea surface elevation (with an accuracy of 10% in the
significant wave heights) acquired from nautical radars in estimating the water depth.
Reichert et al. (1999) and Hessner et al. (1999a) have compared sea state
measurements acquired from shallow water installation of a remote sensing system
based on a nautical X-band radar, to Waverider buoy data, and found that surface
current velocities could be estimate to within an accuracy of ± 0.2 m/s.
Recently, Dankert and Rosenthal (2004) developed an empirical inversion method
for determination of time series of ocean surface elevation, which maps from X-band
nautical radar image sequences in relative deep region. For validation of their result,
the wave elevation time series derived from the inverted radar data sets were
compared with wave records, and acceptable accuracy was established. Takewaka
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and Nishimura (2005) analyzed radar images for run-up analysis during a storm.
Takewaka (2005) also analyzed time averaged X-band radar images to quantify
shoreline position and inter-tidal foreshore slope, while Ruessink et al. (2002)
analyzed images to locate near-shore bar crest. Chowdhury (2007) analyzed the
correlation between water depth echo sounder measurement and water depth X-band
radar deduced. The comparison shows moderate correlation between two depths.
Within this thesis, the comparison between water level from X-band radar-deduced
and water level from gauge measurement will be analyzed during the storm condition
to identify the correlation between both measurements (see, chapter 4).
.
2.3 Erosion and Deposition
The morphodynamical processes in coastal area are affected by tidal currents and sea
state, leading to a transport of sand along the seafloor. Vice versa the tidal currents
are influenced by changes in the bottom topography (SOULSBY 1997). The
continuous observation of areas of high morphodinamycal activity is important in
order to warn of such changes in the flood stream situation and to avoid futher
change or loss of land (WOLFF et al. 1999).
Morphodinamycal changes can be observed by radar. Radar images the small
roughness on the sea surface, causing backscattering (LEE et al. 1995). The sloping
bottom induced horizontal gradients in the tidal current, resulting in a variation of the
surface roughness (ALPERS & HENNINGS 1984). Another effect resulting in the
imaging of the bottom topography is caused by wave breaking in the shallow water
(HENNINGS 1988). Therefore, the backscattering indirectly depends on the
bathymetry. It is known from the analysis of the satellite images that the observable
signatures depend on the tidal currents and the wind situation (VOGELZANG 1997).
In a study by MENN (2002a, b) the effects of eroding and accreting conditions on
the structure of beaches were determined. The eroding shore (Sylt/Germany) is
coarse grained, steeply profiled and receives high wave energy, while the accreting
shore (Rømø/Denmark) is fine grained, flat profiled and receives less wave energy.
The former resembles dynamic intermediate beach types and the latter a dissipative
beach type (Short & Wright 1983).
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The motivation for the observation of the coastal area at Sylt is its high
morphodynamical activity. A sand bar between the Lister Landtief and the Lister
Tief is the process of breaking, which would change the flood stream situation
dramatically. As it is possible to draw conclusion about the bathymetry by
interpretation the observation structures, permanent monitoring of the area would
allow continuous observation of changes in the bottom topography.
Erosion is almost synonymous to the Sylt Island. The entire coast of Sylt has been
severely eroding since a long period of time; accumulation of sand is not seen at any
part of the coast. After 1950 the erosion rate in Westerland-Kampen (north of
Westerland) has been increasing as compared to the southern area (SISTERMANS &
NIEUWENHUIS 2007). During a single storm event it is estimated that about 50,000
cubic meters (± 10%) of sediment is replaced in the area (FLAMPOURIS 2006).
The sediment transport results in a dominant seaward directed cross shore bar,
pointing into the German Bight, vice versa this bar steers the tidal current
surrounding the north end of Sylt and thus it indirectly steers the sediment transport
in the feed back process. The long shore transport along the coast is mainly waveinduced and therefore also alternating in direction. Due to the structural erosion by
wave and tide, the adapted main type of coastal protection is beach nourishment at
the west coastline of the island, the majoring of this sand being lost during storm
surge (AHRENDT 2001).
For the observation of morphodynamic changes at the List Tief area, the changes of
slope in the tidal channel from three different time periods will be analyzed (see,
chapter 4).
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3. Theoretical Background
3. Theoretical Background
Remote sensing is the collecting data about sea surface features without coming into
direct physical contact with them. The last three decades, the originally technologies
developed for military purpose and have been converted for scientific and civil
applications. Many of earth observation missions have been successfully carried out
providing some useful information. Oceanography, hydrology, geology, forestry and
agriculture have been targeted for such applications as hazardous events prevention
and territory management. Many of the sea-state parameters for coastal and
oceanographic researches are observed by remote sensing techniques, including
wave height, water level current field, sea surface temperature, ocean color and
surface wind field (FLAMPOURIS 2006).
Ocean wave remote sensing observation can be applied from the several coasts, ship,
aircraft or satellite. Surface Ocean waves are measured by several different
techniques have become of particular interest in applications where the advantage of
remote sensing is to avoiding direct contact with the water surface and avoiding
structural interference. The sensor type includes infrared sensor, optic sensor and
radar. Radar remote sensing of ocean surface waves may in general be defined as
measuring characteristics of the sea surface by means of electromagnetic waves so
that the sea surface itself not disturbed. The electromagnetic waves transmitted by
the radar antenna are scattered back from the sea surface, modulated in amplitude
and phase or frequency by the interaction with the sea surface motion. This
modulation carries information about sea characteristics, surface waves and currents.
Oceanographic data is extracted from the backscatter signal by sophisticated signal
processing and data analysis (SKOLNIK 1990).
The waves are propagating from open sea toward to the coast. During the storm
condition, the wave action can cause erosion or deposition at the nearshore area.
Therefore, the monitoring of waves at nearshore area is required. These waves can be
monitored by ground based X-band radar. The assumptions of the waves are
described by linear wave theory and it could be inversed for determination of local
bathymetry.
In this chapter, the basic theoretical background of the ground based X-band radar,
the linear theory and the connection with DiSC method will be described.
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3. Theoretical Background
3.1
Microwave
Radar
Remote
Sensing
Applied
in
Oceanography
Radar measures the strength and round-trip time of the microwave signals that are
emitted by a radar antenna and reflected off a distance surface or object. The radar
antenna alternately transmits and receives pulses at particular microwave
wavelengths and polarizations (waves polarized in a single vertical (VV) or
horizontal plane (HH)).
Radar can be operated both day and night. This type of system is known as radar
active system while passive radar measures the electromagnetic radiation emitted by
any radiating source. Microwave radar with wavelength ranging from 0.1 cm to 100
cm, are noted for their ability to penetrate rain, fog and clouds. The spatial resolution
of a radar system depends on the transmitted signal in the range and on the antenna
pattern in direction (LILLESAMD & KIEFER 1994). The azimuth resolution
depends on the microwave wavelength and antenna length; real aperture or the ratio
antenna length to microwave length may be improved by either decreasing the wave
length of electromagnetic wave or by increasing the antenna length. However, the
shorter wavelength radars are affected by sea spray or the rain drops.
Nowadays, remote-sensing techniques at the coastal zone applied to wave and
current measurement with coastal radar have become more important. Coastal radar
used the microwave radar which has frequency range from 3 to 30 GHz and high
frequency radar which has frequency range from 3 to 30 MHz. Both use
electromagnetic waves remotely sense ocean surface current and sea states over
extended areas. The advantage of microwave radar is easy to install, but does not
cover the area as large as it is possible to cover with HF radars. Microwave marine
radars originally used for navigation have been developed to measure the ocean
waves, such as WaMoS (Waves Monitoring System). WaMoS makes ocean waves
and surface currents measurement with microwave marine radar (X-band radar)
based on the spatial and temporal structure analysis of radar images of the sea
surface (REICHERT et al. 1999). These radar images are generated by the
interaction of electromagnetic waves with the surface ripples at grazing incident. The
spatial and temporal variability of the sea clutter information is analyzed in order to
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3. Theoretical Background
extract the wave spectrum and further sea state parameters, such as significant wave
height and peak period.
Although the observation range of coastal radars is not as extensive as satellites, the
superiority of waves measurement by land-based radar lies in its capability to
observe 3D images of the sea state by routine operation, as opposed to 2D
observation made from satellite or aircraft. In addition, the wave monitoring systems
by coastal radars are relatively easy to install and to operate. Thus it would appear
that coastal radars are the potential instruments for the remote sensing activities of
waves monitoring, more extensively in the future.
For the present study, the ground based X-band, microwave radar is used. Details of
the radar system are tabulated in Table 3.1.
Table 3.1: Properties of the X-Band Furuno 1201 nautical radar (ANONYMOUS 1989).
Properties
Value
Frequency
9410 MHz ± 30 MHz
Pulse repetition Frequency
3 KHz
Antenna type
Slotted Wave Guide
Antenna beam width
0.95º
Polarization
HH
Rotation speed
34-40 cir/min
Output power
5 KW nominal
Pulse length
0.05 μ sec
The antenna rotation time allows imaging successively the ocean surface without the
loss of correlation of the image wave fields. This allows acquiring image time series
of ocean wave fields, which have the quality to extract wave describing parameters
by inverse modeling.
3.1.1 Radar Equation
The way to describe the radar principle is the physical definition, as the single most
useful description of the factor influencing radar performance is the radar equation
which gives the range of radar in terms of the radar characteristics. One form of this
equation gives the received signal power Pr as:
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3. Theoretical Background
Pr
§ Pr Gt ·§ V ·
A
¨
¸
2 ¨
2 ¸ e
© 4SR ¹© 4SR ¹
(3.1)
The right side has been written as the product of three factors to represent the
physical processes taking place. The first factor is the power density at a distance R
meters from radar that radiates a power of Pt watts from an antenna of gain Gt . The
numerator of the second factor is the target cross section ı in the square meters. The
denominator accounts for the divergence on the return path of the electromagnetic
radiation with range and is the same as the denominator of the first factor, which
accounts for the divergence on the outward path. The product of the first two terms
represents the power per square returned to the radar. The antenna of effective
aperture area Ae intercepts a portion of this power in an amount given by the product
of the three factors.
3.1.2 Sea Clutter
Ocean waves are imaged by a nautical radar because the long surface gravity wave
modulate the radar backscatter from the sea surface. Thereby the small scale
roughness of the sea surface raises the backscatter of the electromagnetic waves. This
phenomenon is called sea clutter (WETZEL 1990).
Bragg scattering is resonant backscatter that occur when electromagnetic energy
interacts
with
waves
that
have
wavelength
interacting
with
transmitted
electromagnetic waves. At large angels of incidence, Bragg scattering is responsible
for the return, at grazing incidence Bragg scattering criterion being fulfilled by those
wave having a wavelength equal to one half the electromagnetic wavelength. Small
scale capillary waves on the order of 1 to 3 cm provide the source for Bragg resonant
scattering of marine X-band radars. The intensity of backscattered energy is most
affected by magnitude of the wind velocity, the incidence angle of the emitted Bragg
scattering is strongest when the radar azimuth angle is aligned with the wave
direction. This pattern of returned electromagnetic energy is modulated by the large
structures, such as swell and wind sea waves.
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3. Theoretical Background
It would seem a simple matter to characterize sea clutter empirically by direct
measurement of radar returns for a wide variety the radar and environmental
parameters that appear to affect it. Parameters relating to the radar or its operating
configuration, such as frequency, polarization, cell size, and grazing angle, may be
specified by the experimenter, but the environmental parameters are quite another
matter for two reasons. First, it has not always been clear which environmental
variables are important. Even if the importance of an environmental parameter has
been recognized, it is often difficult to measure it with accuracy under real sea
condition, and there are practical and budgetary limits to obtain open-ocean
measurements in sufficient variety to develop any really meaningful statistical
models of clutter. Little wonder that many aspects of sea clutter remain frustratingly
unidentified (SKOLINK 1990).
It is noted that the appearance of sea clutter depends strongly on the size of the
resolution cell or radar footprint. For large cells it appears distributed in range and
may be characterized by a surface-averaged cross section with relatively modest
fluctuations about a mean value. As the size of the resolution cell is reduced, clutter
takes on the appearance of isolated target like, or discrete, returns that vary in time.
At these higher resolutions, the distributed clutter is often seen to consist of a dense
sequence of discrete returns. When the discrete returns stand well out of the
background, as they are seen to do for any polarization but most clearly with
horizontal polarization at small grazing angles, they are called sea spikes and are
common clutter contaminant in this radar-operating regime.
In 1956, however it is observed that at high frequency (HF) wavelength (tens of
meters) scattering appeared to arise from a resonant interaction with sea waves of
one-half of the incident wavelength (CROMBIE 1956), i.e., to be of the Bragg type.
Reinforced by the theoretical implications of various small wave height
approximations and wave tank measurements under idealized conditions, the Bragg
model was introduced into the microwave regime by many researchers. This
produced a revolution in thinking about the origins of sea clutter because it involved
the sea wave spectrum, thus forging a link between clutter physics and oceanography
in what became the field of radio oceanography. However, fundamental conceptual
problems in applying the Bragg hypothesis in microwave scattering, along with
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3. Theoretical Background
recent questions about the validity of its predictions and the possibility of alternative
scattering hypotheses, have reopened inquiry into the physical origins of sea clutter
and how best to model it. This being the case, speculation about models will be kept
to a minimum in the sections on the empirical behavior of sea clutter (SKOLNIK
1990).
3.1.2.1 Backscatter Mechanisms
There are various measuring techniques based on the backscatter theories of radar
signal. Some are based on the analysis of the backscatter intensity of the return radar
signal. Others use both the backscatter intensity and the Doppler spectrum. The
mechanism that leads to a scattering of the electromagnetic waves from the sea
surface depends on the incident angel. At small incidence angles with respect to the
vertical (less than 15°-20°), the main scattering mechanism is quasi-specular, and the
roughness scale with govern the backscattering intensity cover all scales from about
3 times the electromagnetic wavelength. At the moderate incident angle from (20° to
70°), the main processes is the so-called “Bragg resonant process” which is generated
time by the waves on the surface which are of the same order as the electronic
wavelength. At large incidence angles (grazing angle above 70º), the backscattering
is more complex, including shadowing effect and other complex mechanisms. In
some cases the backscattered signal provides “direct” information on the wavelength
of interest, because the Bragg wavelength is of the same order. In other case, marine
radars, airborne, or spaceborne real or synthetic aperture radars, the backscatter is
related to short wavelength of interest such as X-band radar which is used wave
imaging based on Bragg scattering from the small capillary ripples on the surface of
the gravity waves.
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3. Theoretical Background
3.1.2.2 Bragg Backscattering
The radar echo is generated by Bragg scattering, hence wind generated surface ripple
(capillary waves) must be present the back scattered signal will be modulated by the
large surface gravity waves and gravity wave information is derived from the
modulation of backscattered signal.
The Bragg backscattering consists the main theory broadly used for the
backscattering of radar, e.g. ground based or naval radars, ERS SAR and in the
present paragraph the mechanism is described.
As the incidence angle of radar is oblique to the local mean angle of the ocean
surface, there is almost no direct specular reflection except at very high sea states.
Therefore it is assumed that at first approximation Bragg resonance is the primary
mechanism for backscattering radar pulses. The Bragg equation defines the ocean
wavelengths for Bragg scattering as a function of radar wavelength and incidence
angle:
OS
§ Or ·
¨
¸
© 2 sin T ¹
(3.2)
where Ȝs is the sea surface wavelength, Ȝr is the radar wavelength and ș is the
incident angel.
The short Bragg-scale waves are formed in response to wind stress. If the sea surface
is rippled by a light breeze with no long wave present, the radar backscatter is due to
the component of the wave spectrum which resonates with the radar wavelength. The
Bragg resonant wave has its crest nominally at right angles to the range direction.
For surface waves with crest at angle to the radar line-of-sight, as shown at the
figure, 3.1, the Bragg scattering function is:
O 'S
O r sin I
2 sin T
O S sin I
(3.3)
where: O'S is the wavelength of the surface waves propagating at the angle I to the
radar line of sight.
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3. Theoretical Background
Figure 3.1: Scheme to visualize the relation between scattering wave with the length Ȝs and the
electronic wave with the length Ȝr. The relation between those two is observed by (ESA, 1968)
and consist the basic principle of the radar system.
The radars directly image the spatial distribution of the Bragg-scale waves. The
spatial distribution may be affected by longer gravity waves, through tilt modulation,
hydrodynamic modulation and velocity bunching.
Moreover, variable wind speed, changes in stratification in the atmospheric boundary
layer, and variable currents associated with upper ocean circulation features such as
fronts, eddies, internal waves and bottom topography affect the Bragg waves.
3.1.3 Modulation Mechanisms
There are several modulation mechanisms that effects the measurements by the
radar, the integrated effect of the processes are describe in the next three paragraphs
is that one image of low wave field is impressed to the radar signal that is related to
the instantaneous sea surface by a Modulation Transfer Function (MTF). For the
discussion within this thesis, it is only necessary to localize the position of the
moving wave crests and not the retrieve the real shape of the surface. The linear
scaled imaging of the wave crests within the radar backscattered fields is not affected
by the MTF, thus the intense about it is not real strong.
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3. Theoretical Background
3.1.3.1 Tilt
Tilt or electromagnetic modulation occurs when a local tilting of the surface changes
the local incidence angle and thus the wave on the surface that causes Bragg
scattering (WACKERMAN 2000). Tilt modulation is a purely geometrical
phenomenon that is created by gravity waves “tilting” the ocean surface towards and
away from the radar. Radar backscatter increases as the wave is tilted towards the
radar and decrease as the wave is tilted away from the radar. Tilt modulation is most
prevalent when the radar beam is perpendicular to the wave front. Tilt modulation
provides no contribution to the backscatter if the wave crest is parallel to the radar
beam.
3.1.3.2 Hydrodynamics
The sea clutter depends on the hydrodynamic conditions of the area of investigation;
the effect the currents on signal is the most investigated. Hydrodynamic modulation
is caused by change in shape of small-scale waves that cause Bragg scattering.
Capillary waves increase in amplitude, decrease in wavelength on the front of gravity
waves and decrease in amplitude, increase in wavelength on the back gravity waves.
The modulation of small-scale capillary waves on the front of the wave leads to a
higher amount of backscatter on the front part of the wave.
Shipboard observers have reported bands of roaring breakers passing by on an
otherwise smooth surface, presumably produced by powerful surface-current shears
associated with large amplitude internal waves. The general effect of the current is a
change in the surface roughness, which can be expected to give rise to a change in
sea clutter cross section (LONG 1990).
3.1.3.3 Shadowing
Radar shadowing as the image can only display that which is along a line of sight to
the radar antenna. Shadowing occurs when the crest of wave prevent illumination of
the following trough. Thus a “shadow zone” is created between successive crests.
Shadowing is the most prevalent modulating mechanism at high angles of incidence
(DANKERT and ROSENTHAL 2004).
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3. Theoretical Background
The shadowing effect at the image sequences of the coastal radar caused by the shape
of the waves. The waves are characterized by bright signals from the near slopes and
the absence, not illuminated by the radar, of signal by the far slopes. For the sea, it is
likely that effects of shadowing become appreciable for angles of incidence closer to
horizontal that the crest height and sea wavelength. The shadowing of troughs by
crests cause the reduction in expected scattered power. At near grazing incidence
angles, when shadowing is appreciable, it is expected that the top of the crests
contribute significantly to create the effective reflective surface.
3.2 Sea Surface Waves
Ocean surface waves are mechanical waves that propagate along the interface
between water and air. The primarily natural forces are pressure from the atmosphere
(especially through the winds), gravity of the Earth and celestial bodies (the moon
and the sun), earthquakes, the Coriolis force (due to the Earth’s rotation) and surface
tension. The characteristics of waves depend on the driving forces. Tidal waves are
generated by the response to gravity of the moon and the sun and are rather largescale waves. Capillary waves, at the other end of the scale, are dominated by surface
tension in the water. The restoring force is provided by gravity, and so they are often
referred to as surface gravity waves. As the wind blows, pressure and friction forces
perturb the equilibrium of the ocean surface. These forces transfer energy from the
air to the water, forming waves.
The general concept of the mechanism of wind sea-surface wave generation: if wind
skims along the water surface, small perturbations of the near boundary atmospheric
pressure field lead to small perturbation of the water surface. The distorted surface
allows viscous or turbulent energy transport, leading to the growth of waves. Several
theories have developed for detailed explanation of the phenomenon (MILES 1957,
HASSELMANN 1962, PHILLIPS 1966) but still it has not totally been clarified. The
information about the energy distribution of the waves versus the frequency or the
wavelength is illustrated in figure 3.2.
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3. Theoretical Background
Figure 3.2: Classification of ocean waves and their relative energy.
3.2.1 Linear Wave Theory
A regular wave is defined by sine function or sinusoidal (figure 3.3). In order to fully
specify a regular wave, it will be needed its amplitude, ȗ, its wavelength Ȝ or the
wavenumber k=2ʌȜ-1, its period IJ or angular frequency Ȧ=2ʌIJ-1, and in addition its
propagation direction ș and phase at a given location and time.
Figure 3.3: A simple sinusoidal wave
Coastal Geosciences and Engineering, University of Kiel
23
3. Theoretical Background
A sea surface wave is a plane wave and therefore k and ș can be expressed in
Cartesian coordinates as a two-component wave number vector, k = (kx, ky). A linear
sea surface wave is sinusoidal shape. Deviations from this shape are expressed as
nonlinearities. A single sinusoidal plane wave has the form
] ( 4)
GG
GG
¦ Se i ( kr Zt ) ¦ S e i ( kr Zt )
(3.4)
Where, ȗ is the sea-surface elevation in the spatio-temporal domain Ĭ= (x, y, t),
S
] 0 e iI is the spectral Fourier coefficient, where I 0 is the initial phase, S̅ is
0
G
G
complex conjugated of S and k is the wavenumber vector and r
G G
spatial vector. The expression: I I 0 k ˜ r Zt describe the phase I .
( x, y ) is the
By generalizing the above concept, a wave field is defined as the superposition of
single waves and its shape is the sum of n single waves (Figure 3.4).
] ( 4)
¦ Se
G
i ( k n r Z n t )
(3.5)
G
where k n is the nth wavenumber vector, Ȧn is the nth frequency and S n
] 0 e iI , n is
0
the nth Fourier coefficient for the nth wave.
Figure 3.4: Sea-surface obtained from the sum of many sinusoidal waves (derived from Pierson
et al. 1995)
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3. Theoretical Background
3.2.2 Stationarity of Wave Field
In the mathematical science, a stationary process is a stochastic process in which the
probability density function of one random variable X does not change over time or
position. As a result, parameters such as the mean and variance also does not change
over time or position, experimental proved for at least short periods (PRINS 1996).
Therefore, the general definition of the stationarity makes clear that for a wave field
two conditions must hold to fulfill the criterion of stationarity: the local temporal
phase gradient,
wIi
wt
Z i and
wIi
, have to be invariant in time for considered time period:
wt
w] 0,i
wt
0
(3.6)
where Ii is the temporally local phase, ] 0,i is the temporally local amplitude and Ȧi
is the temporally local frequency, which is constant. If one of the above criteria does
not hold for at least one wave of the wave field for the period of the observation, the
wave field is instationary.
3.2.3 Homogeneity of wave field
A stochastic process is defined homogeneous in space if the transition probability
between any two state values at two given locations depend only the difference
between those state values (PRINS 1996).
For a wave field in an oceanic box two condition must hold to fulfill the criterion of
homogeneity: the spatially local phase gradients,
wIi wIi
,
and the total amplitude, y,
wx wy
have to be invariant in space. Defined for the Cartesian coordinates (x,y), the criteria
of homogeneity are
wIi
wx
k x ,i and
w] 0,i
wx
0
(3.7)
And
Coastal Geosciences and Engineering, University of Kiel
25
3. Theoretical Background
wIi
wy
k y ,i and
w] 0,i
wy
(3.8)
0
where Ii is the spatial local phase, ] 0,i is the spatially local amplitude and ki are the
spatially local wavenumber vectors, which are constant. If one of the above criteria
does not hold in the considered oceanic box for at least one wave of the wave field,
the
wave
field
is
inhomogeneous.
The
above-mentioned
processes
are
inhomogeneous processes. The spectral effects due to inhomogeneous and
instationary processes are illustrated in figure 3.5. If a wave field instationary, the
global spectral signal is smeared vertically to other frequencies (green dot); if a wave
field is inhomogeneous, the global spectral signal is smeared to other wavenumbers
horizontally (red dot).
Figure 3.5: spectral instationarity and inhomogeneity illustrated in a 2D k-Ȧ section. (SENET
2004).
3.2.4 Dispersion relation
Assuming a non-viscous, incompressible and homogenous liquid, e.g. water, the
dispersion relation of sea surface waves is derived from Eulerian equation of motion,
26
Coastal Geosciences and Engineering, University of Kiel
3. Theoretical Background
the continuity equation and the dynamic and kinematic boundary conditions of the
dispersion relation is given in (WINKEL 1994).
The phase speed Cp and the group speed Cg are given by
Cp
Z
k
or C p
O
W
(3.9)
dZ
dk
(3.10)
And
Cg
dO
or C g
dW
The phase speed Cp determines the speed of propagation of a single wave
component, and the group speed determines the propagation of the wave field’s
energy. In extremely shallow water which have wavelength Ȝ > 0.1d, Cg = Cp; in the
deep water which have wavelength Ȝ <
d
, the condition C g
2
Cp
2
holds.
The dispersion relation describes the dynamic relation between wavenumber k and
angular frequency Ȧ and determine the phase speed, speed of propagation of a wave.
The term “normal” dispersion implies that longer waves have a higher phase speed
and shorter waves. This performance holds for capillary waves. The linear dispersion
relation for free gravity sea surface waves, if the surface is ignore is given by
G
Z~ (k )
G
gk tanh(kd ) k ˜ u c
(3.11)
where g is the gravitational acceleration, d is the water depth, uc is the near surface
current.
gk tanh(kd ) ,
At the equation (3.11) the first term is called intrinsic frequency, 9 r
G
and the second term is called the Doppler frequency, Z D k ˜ u c , indicates the effect
of near surface current. Following (3.11), the accelerations which force an elevated
G
particle to move back to initial position, ] is g , this happens to waves longer than
0.1 m. when the waves O < 0.1 m, only the surface tension of water has a significant
effect of small waves, those waves are called capillary gravity waves and the relation
Coastal Geosciences and Engineering, University of Kiel
27
3. Theoretical Background
which describes them take account also the surface tension, in this case they are
G
ignored. The water depth (d) and the near surface current vector ( u c ), are free
parameters which influence the shape of the dispersion shell in the wavenumber
frequency domain ( : ). Therefore the shape of the dispersion shell can be used to
inversely determine these parameters.
The dispersion relation generates a shell in the 3Dȍ domain. The intrinsic dispersion
shell is symmetric about the rotation axis, figure 3.6. The intrinsic dispersion relation
has two solutions, 9 and 9 . These two solutions are redundant, a consequence of
the symmetrical attributes 9 = - 9 of the Fourier transformation.
G
G
Due to the redundancy of the dispersion shell 9 ( k ) and - 9 ( k ) are hermetic and
only one of the shell is needed to describe the energy of wave fields in the ȍ domain.
Figure 3.6: Positive and negative dispersion relation of linear deep-water surface-gravity waves
in 3Dȍ domain, (SENET 2004)
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Coastal Geosciences and Engineering, University of Kiel
3. Theoretical Background
3.2.5 Water Depth and Near Surface Current
G
If a near surface current, u c is present, waves are Doppler shifted. The Doppler shift,
Z D leads to a frequency shift of Z . If a current is directed in a direction opposite to
that a wave, the wave’s absolute, in the inertial coordinate system of the observer,
frequency is increased and vise versa. The deformation of the dispersion relation due
to the Doppler effect is illustrated at figure 3.7c.
1
For deep-water waves, defined by the condition d > O , the approximation tanh(kd)
2
G
§ 1 holds and can be substituted into 3.11. By assuming u c 0 , the deep-water wave
solution is as follows:
] (k )
gk
(3.12)
In shallow waters, where d is small comparing to Ȝ, the shallow water dispersion is:
] (k )
k gk
(3.13)
G
is obtained when the approximations tanh(kd) § kd and u c
0 are substituted into
(3.11).
Figure 3.7: Dispersion relation of linear surface-gravity waves in 3D ȍ domain: a) intrinsic
deep-water dispersion shell, b) intrinsic shallow water dispersion shell and c) Doppler shifted
deep-water dispersion shell influenced by near-surface current, (SENET 2004)
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29
3. Theoretical Background
3.3 Dispersive Surface Clasificator
The Dispersive Surface Classificator (DiSC), is a recently presented algorithm
(SENET et al. 2008), which analyses image sequences for the determination of
physical parameters on a local spatial scale, it consists a local analysis method, which
allows the analysis of inhomogeneous image sequences of a dynamic and dispersive
surface. The basic idea of the method is that in shallow waters wave fields become
inhomogeneous due to spatially variable bathymetries. Local change of the wave
field, containing the local bathymetry information, therefore must be taken into
account.
For analyzing the radar data, software DiSC is used which was developed at the
Radar Hydrography Department of the GKSS and commercialized product by Vision
2 Technology GmbH, partner of the Geesthachter Innovation und Technologie
Zentrum (GITZ).
The basic steps of DiSC are the following:
x
Transformation of the image coordinates from polar to Cartesian.
x
Application of 3-D discrete Fourier transformation on the image sequences.
x
Decomposition of the complex-valued image spectrum for the separation of the
wave signal from the noise and Directional and dispersion separation of the
complex-valued spectrum into spectral bins at 2D wavenumber planes of
constant frequency by using filtering techniques.
x
2D inverse Fast Fourier Transformation (2D FFT-1) of the spectral bins yielding
complex-valued, one-component spatial maps in the spatio-frequency domain.
x
Calculation of spatial maps of local wavenumber vectors from the onecomponent images of constant frequency by using the phase of complex-valued
one component images.
x
Use of the spatial maps of local wave number vectors and power for the
calculation of spatial hydrographic parameter maps.
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3. Theoretical Background
Figure 3.8 Scheme of the procedural and data flow of DiSC (FLAMPOURIS 2007)
3.3.1 Assumptions of DiSC
The requirements for the application of DiSC are, stationarity and validity of the
multi component image model (SENET et al.2003).
Stationarity: The image process analyzed by DiSC has to be stationarity. Stationarity
implies the temporal invariance of a signal. Assuming stationarity, DiSC can treat the
spatial Fourier decomposition of the distinct frequency components independently,
with the complex-valued spatial image at a constant frequency.
Validity of the multi-component image model: For inhomogeneous images the
amplitude or the spatial phase gradients (i.e. the local-wavenumber vectors) vary.
This information is only implicitly included in the coefficients of the Fourier
decomposition. To enable explicit analysis, the spatial Fourier decomposition is
transformed to an image representation, composed of the superposition of 2D jointly
amplitude-frequency-modulated, local coherent, analytic signals, multi-component
image model.
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3. Theoretical Background
3.3.2 Input Parameters
A 3D image sequences as the input data set of the DiSC has to be analyzed, each of
the radar image sequence, has three dimension which are the x (easting), the y
(northing), and the time t (as number of images), this information are imported at the
beginning of the process to the DiSC. In addition to them, the number of pixels at the
x and y-axis, the real size of each pixel and the rotation period of the antenna are
imported.
3.3.3 The algorithm of DiSC
The signal to noise ratio, broadly used method is based on spectral filtering and the
analysis of the real-valued 3D gray variance spectra. The spectral phase, which
contains information on the local image structure (OPPENHEIM and LIM 1981), is
not used. For the determination of the physical parameters on a local spatial scale,
recovers the spatial structure of the image sequence from the complex-valued 3D
spectrum. The core of the local analysis method is a decomposition of the complex
valued 3D image spectrum, which is followed by a 2D FFT-1 into the spatiofrequency domain.
The algorithm is a 5-step method:
1. 3D Fast Fourier Transformation: A discrete 3D Fourier Transformation (3D FFT)
can be acquired by the decomposition into 1D FFTs. A 3D FFT using the world
and spectral coordinates and the result of process is a discrete complex valued
image spectrum of the 3D domain. The discrete grid resolution of the spectrum is
calculated the spatio-temporal extension of the initial image sequence. By the 3D
FFT, the initial dimension x, y, and t are transformed to kx, ky, and Ȧ. The result
of the x-dimension is the x-component of global wavenumber, of the y-dimension
is the y-component of global wavenumber and of the time t is the frequency. By
the result of process, the choice of the power of the backscatter and the minimum
and maximum bin, where the energy lays, take place.
2. Spectral decomposition: The aim of the spectral decomposition of the spectral
signal of the inhomogeneous wave field is the division of the signal into onecomponent images containing separated and analyzed parts of the wave field.
The
32
spectral
decomposition
technique
DDF-S
(Directional
Coastal Geosciences and Engineering, University of Kiel
Dispersion
3. Theoretical Background
Frequency-Separation) is based on the combination of frequency separation
taking a kx - ky slice of the 3D wavenumber-frequency spectrum and a directional
wavenumber band pass filter in kx _ ky centered on the dispersion shell (dispersion
filtering), yielding a spectral DDF bin. The principle of DDF-S is outlined in
figure 3.9.
Dispersion filtering is required because of the nonlinearity of radar imaging of
the sea surface waves. The nonlinear modulation transfer function (MTF) can be
expanded in a Volterra series (CHERRY 1994), creating sum-differences and
harmonic signals in addition of the linear fundamental mode in the radar image
spectrum. The linear (fundamental) mode is selected by dispersion filtering. The
remaining spectral smearing is caused by the inhomogeneity of analyzed area.
Figure 3.9: Spectral decomposition by filtering (SENET 2004)
3. Inverse 2D FFT: Complex valued one component images are calculated by
transforming the filtered frequency slices of wavenumber planes of the 3D image
spectrum into the spatial domain, using a 2D FFT-1. The spectral decomposition
and inverse 2D FFT yields complex-valued spatial one-component images. These
complex-valued one-component images are illustrated as power phase of separate
part of the wave field.
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33
3. Theoretical Background
4. Calculation of local wavenumber: Determination of spatial maps of localwavenumber vectors is achieved using the phase of the complex-valued onecomponent images. Initially an approximate version of the multiple-signal
classification algorithm (STOICA and NEHORAI 1989, HAVLICEK et al. 1996)
was used to estimate local wavenumber vectors. The method provides complexvalued wavenumber vectors.
5. Calculation of hydrographic parameters maps: In the variance spectrum, the
linear portion of signal energy of the waves is localized on the dispersion shell
surface waves. Therefore the filling up, the instant depth, of the water mass could
be calculated for each grid cell. The only parameter that has to be defined is the
minimum number of the regression coordinates that is by default 10. More detail
about this technique at (FLAMPOURIS 2006).
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Coastal Geosciences and Engineering, University of Kiel
4. Methodology
4.
Methodology
The complete methodology of the investigation is described analytically in this chapter.
The methodology is divided into two sections, Data Acquisition (sec. 4.1) and Data
Processing (sec. 4.2).
4.1 Data Selection
The first step is the selection of radar data which depends on the purpose of
investigation. In this section, the experimental setup, the used radar data for processing
and the post processing of the DiSC results are described briefly.
4.1.1 Experimental Setup: Sylt
The radar station was mounted near the lighthouse of List West on the island of Sylt in
German bight. The areas covered by radar images are part of List West, Lister Landtief ,
and Lister Tief. The utilized system for the acquisition of the sea surface is a softwarehardware combination, presented by NIETO BORGE et al, (1999), as a part of the Wave
Monitoring System (WaMoS), consisting by a Furuno FR 1201 (FURUNO MANUAL
1989), a WaMoS II analog digital converter and a WaMoS II software package for the
acquisition of the radar image sequences. The radar is ground-based nautical X-band
radar with horizontal polarization (HH), mounted 25m above the NN. The radar was
mounted in the year 2000 and the range covered circle of about 2 km radius.
In addition during the observation period a meteorological station was in operation.
4.1.2 Wind Data
Wind parameter is used as indicator of the weather condition in the investigation area.
The available row data was mounted from 1999 until 2007, with gaps. It is important to
be emphasized here that the intensity of the backscattering depends on the wave
conditions and wind, as the generating force is determined. The selection of the analysis
wind data during the storm conditions are proposed to identify the influence of the wind
in the investigation area.
The wind data was taken from meteorological station of the radar station. Finally, the
two data sets at the winter periods with the highest wind velocity of 8 Beaufort (18 m/s)
Coastal Geosciences and Engineering, University of Kiel
35
4. Methodology
and one data set at summer period with the highest wind velocity of 6 Beaufort (15 m/s)
were chosen to identify the effect of wind behavior toward the water level.
4.1.3 Radar Data
During the period of investigation radar sequences, which consisted by 256 single
images were acquired with a time interval of 1.8 s, which is equal to the antenna rotation
time. Thus, the total sampling time was approximately 8 minutes. The polar images
cover a radius of approximately 2 km, were interpolated to a Cartesian grid with a cell
size of 6.82 m x 6.82 m, corresponding to the spatial resolution of the radar. The number
of pixel for one image is 288 x 288. The exact specification of the Cartesian grid of the
nautical radar image sequences are listed at the table 4.1. The antenna rotation time
varies from sampling to sampling but lies near the 1.8s; the reason of the variance is the
wind impact to the antenna.
Firstly, the commonly and the most difficult part of the marine sciences is the acquisition
data, the rough and many times unforeseen circumstances influence or destroy the
equipment, i.e. the lightning consists one of the most common factors of the radar
destruction. A second reason is the huge storage capacity that is necessary for the row
radar data, every sampling need about 90Mb and only lately the technology permits in
small volume high storage capacity which is useful in the field. Also the archiving of all
these terabytes of row data confronts several problems, mostly at the hardware; enough
data were corrupted by hardware malfunction (FLAMPOURIS 2006).
Finally, the three different storm periods (26th-27th February 2002, 7th March 2002 and
28 October 2002) was chosen for comparison between radar measurements and gauge
measurement in the investigation area to identify the tidal signature and morphodynamic
changes.
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4. Methodology
Table 4.1 specification of the Cartesian grid of the ground based nautical radar images sequences.
Number of pixel in x-direction (west-east) Nx
288
Cartesian-grid pixel resolution in x-direction (west-east) ǻx
6.82m
Spatial length in x-direction (west-east) X
1964m
Number of pixel in y-direction (south-north) Ny
288
Cartesian-grid pixel resolution in y-direction (south-north) ǻy
6.82m
Spatial length in y-direction (south-north) Y
1964m
Number of images per image per image sequences Nt
256
Temporal resolution (antenna-rotation time) ǻt
1.8s
Temporal length of an image sequence T
460s
4.2 Data Processing
After the output data from DiSC processing (processing of bathymetric data) were
evaluated. The first step was the optimization of the reliability of the result according to
the depth and number regression coordinate. The second step is the identification of the
tidal cycle from the calculated sea water level and averaging each time steps of one tidal
cycle from the difference time periods (three periods) of analysis for identifying the
accuracy of the results and to establish one common reference every one period to make
water level values to be comparable. The third is regression analysis between radar and
gauge water level; the fourth step is identified the time lag between water level
measurement in List Westerland and water level measurement in List Tief; the fifth step
is visualized the average bathymetry; the sixth step is defining the cross section at the
tidal channel, the seventh step is water depth analysis over the cross section, and the final
step is slope analysis over the cross section to identify the morphodynamic changes in
the area of investigation. The data processing is illustrated at figure 4.1.
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37
4. Methodology
Processing of bathymetric data
Optical control of the
calculated depth patterns
3m ” depth ” 18m
&
Reg point • 40
The filtered data are
stored
Procedure 1
Procedure 2
Visualization average
Bathymetry maps
Identification of the tidal cycle
Find the correlation between
radar and Gauge water level
with regression analysis
Defining cross section
Water depth
analysis over
cross section
Time lag analysis with crosscorrelation function
Slope analysis
over cross
section
Final Visualization of
the results
Figure 4.1 Flow chart of data processing consist 2 procedure, procedure 1 as the investigation of
theoretical accuracy of DiSC and procedure 2 as the observation of morphodynamic changes.
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Coastal Geosciences and Engineering, University of Kiel
4. Methodology
4.2.1 Export of Data
The final result of DiSC software is a text file, in which are stored the coordinate of
every cell for which has been calculated the instantaneous water depth, the number of the
regression coordinates, the calculated depth and current vector. For the further
processing of the data, it was necessary to export the data to create a new file, which
include all the results. For this reason, a programming in the PV-Wave has been
developed. FLAMPOURIS (2006) was made the program which is consisted by 6
subroutines, the basic concept is that the complex grid of the area of analysis is created,
the coordinates of each of the results and the output is one file where are stored the
results at the whole grid. The structure of the program permits to the user to define the
check of the number of coordinates and the export any calculated variable, number of
regression coordinates depth.
It is evident that the applicability of DiSC depends on the wave condition, as a method
requires waves, long enough, to be influenced by the sea bottom. The reason of filtering
according the number regression coordinate (<40) is at the low frequencies, the real
signal cannot be distinguished from the noise and has nonlinear effects as produced by
wave group (SMITH et al.1996). As result, the dispersion relation does not model the
waves. Moreover, the program is also filtering the depth less than 4 m, the reason is that
the waves are not anymore dispersive at the very shallow area due to wave breaking in
the other words the linear wave theory is not valid at the very shallow area.
4.2.2 Identification of the Tidal Signal
The identification of the tidal cycle consist a common (BELL 1999), (ROBINSON et al
2000) way to control the whole series of the image sequence analysis and the
comparison with gauge measurement consist strong evidence about the reliability of the
results. In this case, the accuracy of DiSC water level result was identified with
confidence interval of variance by assuming one grid cell equal one degree of freedom
and using 95 % level of confidence. Chi-squared was used to calculate the upper and
lower limits as confidence interval of variance. Chi-squared based on the normal
distribution which is approached method at the wave field area. ALPERS &
HASSELMANN (1978) has proven that the normal distribution is approached method to
identify wave characteristic.
Coastal Geosciences and Engineering, University of Kiel
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4. Methodology
The purpose of comparison between tidal gauge and DiSC is to virtualize the parallel
trend for both water levels as the tidal signature. Two procedures from DiSC water level
was examined as comparison with gauge water level. The first steps for the estimation of
the tidal cycle were average the calculated the sea levels of 81 neighboring cells around
the point 3460944.34, 6103240.84 (high degree of freedom). To decrease degree of
freedom, the chi-squared was used to identify the accuracy of DiSC result at the small
area (the area less than at the first step). By decreasing degree of freedom, the variance
will be increased. The second step were average the calculated the sea levels of
homogenous field area by filtering ± 0.25 m from 81 neighboring cells to define the
gentle slope. They have been plotted for the twelve hours (one tidal cycle) of each period
of analysis and take to common reference for each time step.
4.2.2.1
Confidence Interval of Variance
The Chi-squared (Ȥ2) distribution refers to a sum of square random variables, (X12 + X22
+X32 +…+ Xn2). Where n is N (0, 1) variable, it is normal with mean (μ) of zero and
variance (ı2) of one. The chi-square distribution (appendix V) is tabulated according to
degree of freedom (Ȟ) and has mean (μ) = Ȟ and variance = 2Ȟ.
To find the confidence interval for a sample of n observations, the sample variance is
calculated first:
s2
1 n
(
x
x
¦ i )2
n 1 i 1
(4.1)
To describe the variability in this function from one sample to the next, one introduces
the corresponding random S2 where:
S2
_
1 n
(Xi X ) 2
¦
n 1 i 1
(4.2)
If the Xi are independent N (μ,12) random variables, it must be shown that (n-1)S2 is
distributed as a chi-square with Ȟ = (n-1) degree of freedom. The term degree of freedom
is used here in the same sense as it in statistical mechanics. Thus, for any set of n
_
observation there will only be (n-1) independent deviation ( X i - X ) since their sum is
zero from the definition of the mean.
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Coastal Geosciences and Engineering, University of Kiel
4. Methodology
Usually the observations will be assumed to be N (μ, ı2). In this case, Xi/ ı will be N (μ
/ı, 12) and so the random variable will have a chi-square probability density function
with Ȟ = n – 1.
(n 1)
S2
V2
1
V2
n
¦(X
i
X )2
(4.3)
i 1
Since ȞS²/ı² is distributed as ȤȞ², probability limit of the form
­ § D · vS 2
§ D ·½
Pr ® FQ ¨1 ¸ 2 d FQ ¨ ¸¾ 1 D
2¹ V
© 2 ¹¿
¯ ©
(4.4)
Rearranging it follows that the random variables ı²/ S² satisfies
½
­ Q
V2
Q
Pr ®
2 d
¾ 1D
FQ (1 D / 2) ¿
¯ FQ (D / 2) S
(4.5)
Plot of the upper and lower limits Ȟ/ȤȞ (1 – Į/2) and Ȟ/ȤȞ (Į/2) are given in the appendix V
for Į = 0.01, 0.05, and 0.2 and for 3 ” Ȟ ” 100.
4.2.3 The Regression Analysis of Water Level
Regression analysis is a statistical tool for the investigation of relationships between
variables. In this section, Regression analysis is used to show the correlation between
radar and gauge water level measurements.
By determining correlation coefficient (corr), it can be shown the significance
correlation between both water levels. The corr value has range from 0 to 1, which
reveals how closely the correlation is. A trend line is most reliable when its cross
correlation value is at or near 1.
To find the correlation coefficient from both water levels, it must be first estimate the
covariance: μy
cov( x, y )
1 n
¦ ( xi P x )( yi P y )
ni1
(4.6)
where n is number of observation, xi is the gauge water level with mean P x and yi is the
radar water level with mean P y .
So the correlation coefficient:
corr( x , y )
cov( x, y )
V x ,V y
(4.7)
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4. Methodology
where corr( x , y ) is correlation coefficient, V x is variance of gauge water level and V y is
variance of radar water levels.
4.2.4 The Time Lag Analysis between List Westerland and List Tief
The cross-correlation function was used to determine time lag between List Westerland
and List Tief water level by comparison the water level in the both area with the same
time (local time). The cross-correlation function is defined as:
N k
¦ (x
r x , y (k )
t
x )( y k t y )
t 1
N k
¦ (x
(4.8)
N k
t
x)
¦(y
2
t 1
k t
y)
2
t 1
where r x , y (k ) is cross-correlation function, xt is the water level in the List Westerland
at time t, and x is the mean of xt over t. yk t is the water level in the List Tief at time
k+t, and y is the mean of yk t over t. N is the number of time points and k is the time
delay.
The r x , y (k ) value has range from -1 to 1 which reveals correlation between both
measurements. The calculation and comparison of statistical significance values at all
delays within one tidal cycle, and define the delay with the largest value as a “lag”. The
most trivial case of cross-correlation between two stochastic processes occurs when the
cross-correlatin function is identically zero for all lags. This implies that the two
measurements are completely uncorrelated. If the correlation negative, the two
measurements will tend to be mirror images of each other, which is positive change in
one measurement are associated with negative changes in the other and independent of
each other. If the correlation positive, the two measurements are either both positively
correlated or both negative correlated.
The program was used to calculate the difference time lag between List Westerland and
List Tief such as PV-Wave. The program consist 3 subroutines. The basic concept is
comparing the water level data from each time steps. The routine from PV-Wave is
showed in the Appendix IV.
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4. Methodology
4.2.5 Visualization Average Bathymetry Map
The mean bathymetry for each time period was calculated by averaging the water depth
of a tidal cycle. Golden software Surfer was used to construct the bathymetry map for
each period, see chapter 5. The bathymetry map consist two-dimensional representation
of the three-dimensional data. The first two dimensions are the x (easting) and y
(northing) coordinates, and the third dimension, depth, is represented by lines of equal
value. The relative spacing of the contour lines denotes the relative slope of the surface.
The area between the contour lines contains only grid nodes having depth values within
the limits defined by two enclosing contours. The contour interval is defined as the
difference between two contours. Each depth value denotes with difference color in the
bathymetry map. Depth contour are given at 1 m interval. The grid size of the maps is
the same with grid size of the DiSC. It is high possible resolution and the number of cells
is 40 x 40.
The assumption of averaging over one tidal cycle is that the mean value of depth is
constant. Thus, the comparison between three periods is easier to identify.
4.2.6 Defining Cross Section
After the bathymetry maps were created from the averaging water depth, the next step is
the creation of the cross-section in the tidal channel. Two cross-sections were created for
each bathymetry map which are cross-section A-B and C-D. The length cross-section AB is 490.91 m and B-C is 286.6 m (figure 5.5). The points A, B, C, and D lies at the GK
coordinate (3461435.28; 6102831.77), (3460944.37; 6103322.68), (3460944.37;
6103363.59), and (3460617.09; 6103690.87) respectively.
4.2.6.1 Depth Analysis over Cross Section
As the water level fluctuates during a tidal cycle, the comparison of water depth over the
cross section at three different periods can show the variation of water depth in the tidal
channel (figure 5.5).
The common reference is needed as indicator for comparison between the three
difference time periods. By calculating the average water depth of 2002 from the tidal
gauge in List Westerland as a common reference the comparison of the water level from
Coastal Geosciences and Engineering, University of Kiel
43
4. Methodology
different period is possible to investigate. Therefore, the morphodynamic changes can be
identified in the area of investigation.
4.2.6.2 Slope Analysis over Cross Section
The identification slope over the cross-section from grid cell to grid cell was calculated.
The slope is defined as:
D
§ 'L ·
arctg ¨
¸
© 'd ¹
(4.9)
where D is the slope angle in degree, L is the distance over the cross-section and d is
water depth over cross-section.
The morphodynamic changes such as erosion or deposition in the area of investigation
can be estimated with the comparison of slope between there difference time period
(figure 5.6).
44
Coastal Geosciences and Engineering, University of Kiel
5. Results
5
Results
In the current chapter, the results of the investigation are presented. The
methodology of the investigation has been presented, extensively in chapter 4. Three
periods of 12 hours (one tidal cycle); period 1: from 26th-27th February 2002, period
2: on 7th March 2002 and period 3: at 28th October 2002 have been chosen. The area
of investigation is the ship channel in Lister Tief. The three different periods have
been used as example of different wind and wave conditions (see chapter 4.1.2). The
area of investigation approximately covers 2.5 km2.
The results of period 1 are illustrated at figure 5.1; the blue line denotes average
water level every 30 minutes of time series derived as DiSC resulting one tidal cycle.
In figure 5.1a, each of time series have been normalized by subtracting the mean
value of 81 neighboring cells at the point, GK coordinates (3460944.34 m,
6103240.84 m) which covers approximately 0.11 km2. The bars on the DiSC results
show the confidence interval by assuming one grid cell equal to one degree of
freedom and using 95% level of confidence, (see chapter 4.2.2). The accuracy of
DiSC has been checked by decreasing the degree of freedom. The reason of
decreasing the degree of freedom is to increase the variance of averaging data set
which is used as interval limit for comparing with tidal gauge. In figure 5.1b, the
DiSC result in the homogenous field area by filtering ± 0.25 m from the 81
neighboring cells. The pink line as the gauge measurement denotes the 10 min
average every 30 minutes of the time series of water level in Westerland, which have
a shifted 1 hour lag due to the distance. All the water level every one time step takes
into common reference by subtracting with the average water level values, to obtain
the results more reliable.
The comparison between the DiSC result and the gauge measurement on figure 5.1
has the similar general trends. In period 1, water level around homogenous field area
(part “b”) is the best result from the other graph.
The results during period 2 which have time steps every one hour is showed at figure
5.2. The comparison between DiSC and gauge water level is exhibited the difference
result with the period 1. At the period 2, water level in the homogenous field area
(part “b”) is presented the best result.
Coastal Geosciences and Engineering, University of Kiel
45
5. Results
a.
4
3
2
Water Level (m)
1
0
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
0:00
1:00
2:00
3:00
4:00
5:00
0:00
1:00
2:00
3:00
4:00
5:00
-1
radar
-2
gauge
-3
-4
Time (UTC)
b.
4
3
2
W ater Level (m)
1
0
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
-1
-2
radar
gauge
-3
-4
Time (UTC)
Figure 5.1: Graph representing the tidal cycle during period 1 at 26th-27th February 2002 after
subtracting the mean water level of the series from every time step. The pink line is tidal gauge
measurement in Westerland and the blue line is the estimated tidal cycle from radar sequences.
The bars show confidence interval of variance. a. the average radar water level at the 81
neighboring cells around the point (3460944.34, 6103240.84); b. the average radar water level
after filtering with ± 0.25 m at the 81 neighboring cells.
46
Coastal Geosciences and Engineering, University of Kiel
5. Results
a.
4
3
2
Water Level (m)
1
0
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
14:00
15:00
16:00
17:00
18:00
-1
radar
-2
gauge
-3
-4
Time (UTC)
b.
4
3
2
W ater Level (m)
1
0
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
-1
-2
radar
gauge
-3
-4
Time (UTC)
Figure 5.2: Graph representing the tidal cycle during the period 2 at 7th March 2002 after
subtracting the mean water level of the series from every time step. The pink line is tidal gauge
measurement in Westerland and the blue line is the estimated tidal cycle from radar sequences.
The bars show confidence interval of variance. a. the average radar water level at the 81
neighboring cells around the point (3460944.34, 6103240.84); b. the average radar water level
after filtering with ± 0.25 m at the 81 neighboring cells.
Coastal Geosciences and Engineering, University of Kiel
47
5. Results
At the figure 5.1 and 5.2, the confidence interval shows asymetry between upper and
lower limits, because they have different behavior as functions of different equation
(Appendix V).
We compare in-situ gauge measurements of one tidal cycle with: 1.the water level
deduced by the radar measurements in 81 neighboring cells area (blue dots) and 2.
The water level at homogenous field area (green dots). Figure 5.3 show these
comparisons, the most significant correlation (0.77) was found for water level at 81
neighboring cells.
1.5
1
Radar (m)
0.5
0
-0.5
-1
Corr = 0.77
81 neighboring cells area
Corr = 0.39
homogenous field area
-1.5
-2
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Gauge (m)
Figure 5.3: The correlation coefficient produced by comparison between gauge water level and
radar water level at the whole area, 81 neighboring cells, and homogenous area.
Cross correlation analysis was used to determine the time lag between List
Westerland and List Tief, the result of the analysis is illustrated at figure 5.4. The
blue bar denotes the cross correlation coefficient from between water levels (DiSC
and gauge). During the period 1 (figure 5.4a), the time lag is 1.5 hours. The same
result also shows for period 2 (figure 5.4b) which has time lag 1 hour.
48
Coastal Geosciences and Engineering, University of Kiel
5. Results
a.
1
0.8
0.6
Cross correlation coeficient
.
0.4
0.2
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
-0.2
-0.4
-0.6
-0.8
-1
Time Lag
b.
1
0.8
Cross correlation coeficient
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
9
10
11
12
-0.2
-0.4
-0.6
-0.8
-1
Time Lag
Figure 5.4: Cross correlation analysis between water level in List Tief (radar deduced) and
water level in List-Westerland (gauge deduced) with the same local time. The blue bars show the
cross correlation coefficient for both water levels. a. cross correlation at 26th-27th February
2002); b. cross correlation at 07th March 2002.
The average bathymetries of time series (one tidal cycle) for three different time
observation during the period 1, period 2 and period 3 were calculated. Period 1 at
figure 5.5, period 2 and period 3 at Appendix VIII is presented the results of depth
calculation. The interval of isolines is 1 m. The R symbol on the bathymetry map
indicates the radar position.
For the qualitative observation of sediment deposition or erosion during the three
storm periods, are taken the cross sections as indicated in figure 5.5 from A to B and
C to D (Appendix VI) which is started in the shallow area (4 m depth) and cross the
channel (11 m depth).
Coastal Geosciences and Engineering, University of Kiel
49
5. Results
Figure 5.5: Depth of the area of investigation during the storm period (26th-27th February 2002),
as a result of averaging the calculated depths for 12 hours. The R symbol is the radar position.
The white dot is the cross section A-B and C-D.
For comparison the water depth over cross section, the common reference level is
needed; it is calculated by using the simultaneous water depth measurement in
Westerland. With this reference the direct comparison is possible. The figure 5.6 is
illustrated different water depth at three periods over cross section A-B. The blue line
represents the water depth at the period 1, the pink line is period 2 and the green line
is period 3. The difference water depth over cross section during period 1, 2 and 3 is
approximately 0.5 m at the distance 150 m till 400 m from the point A.
50
Coastal Geosciences and Engineering, University of Kiel
5. Results
0.5
0
-0.5
feb/26/02-feb/27/02
march/07/02
oct/28/02
-1
-1.5
-2
Depth (m)
-2.5
-3
-3.5
-4
-4.5
-5
-5.5
-6
-6.5
-7
A0
25
50
75
100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
B
500
Distance (m)
Figure 5.6: The comparison of depth at the cross section A-B during the three difference
periods; the reference is defined as the average of water level in 2002.
The slope variation during three difference time periods at the cross section A-B is
illustrated at figure 5.7. The blue line represents the slope at period 1, the pink line is
period 2 and the green is period 3. The nearshore area which is the east side at the
distance 81.81 m was changed significantly at the three periods. At the period 1,
period 2 and period 3 the slopes are 0.41, 0.07, and 0.7 (degrees). The changes in the
slope for three periods indicate deposition and erosion in the shallow area (4m – 7m).
1
feb/26/02-feb/27/02
march/07/02
oct/28/02
0.9
0.8
Slope (degree)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
A
0
25
50
75
100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
B
Distance (m)
Figure 5.7: The comparison of the slope over the cross section (A to B) for the three different
periods.
Coastal Geosciences and Engineering, University of Kiel
51
5. Results
52
Coastal Geosciences and Engineering, University of Kiel
6. Discussion
6. Discussion
The present investigation is constituted by two main parts: 1.The investigation of the
theoretical accuracy of DiSC results in its application as radar tidal gauge and, 2. the
observation of the morphodynamic changes over the tidal channel.
The water level result every 30 minutes and hourly from different time period is at
figure 5.1 and 5.2 respectively. The general comment is the tidal gauge measurement
lays always in the confidence limits of the DiSC results; hence in term of statistics,
the radar deduced water level is acceptable. The confidence interval proved that the
DiSC result could be used as virtual tidal gauge. An interesting result is shown from
both periods. At the period 1 and period 2, the best result is illustrated in
homogenous field area.
At the period 1 the influences of the gradient in atmospheric pressure to the water
level (inversed barometric phenomena) and the wind speed (15-18 m/s) are identified
as the addition source of error at least for the first 3 hours of the observation (figure
5.1). For the period 2, the trend of the tidal cycle is identified by DiSC result. The
ebbing is monitored satisfactory but during the flooding there is underestimation of
the water level during the last 3 hours, probably due to the wind direction which is
suddenly changing from the West direction (280º from North) to North-West
direction (320º from North) (Appendix III).
The accuracy of DiSC result with gauge measurement is also identified with
regression analysis (figure 5.3). At the 81 neighboring cells area shows significant
correlation. It is proved that the wave at homogenous area is enough to detect the
water depth.
The determination of time lags due to the distance (17 km) by comparing the time
series between water level from gauge measurement in List Westerland and water
level from radar measurement in List Tief in the same local time shows interesting
results
(figure
5.4).
According
to
tidal
calendar
(BUNDESAMT
FUR
SEECHIFFAHRT UND HYDROGRAPHIE 2002) the time lags between both places
is 1 hours. To obtain more precise result about the time lag between two time series,
it is necessary to have longer in time observation. The comparison results from
period 1 and 2 have also proved that the time lags are 1.5 hours and 1 hour,
Coastal Geosciences and Engineering, University of Kiel
53
6. Discussion
respectively. The differences in the time lag could be due to the meteorological
conditions and the extensive (0.5 and 1 hours) sampling interval. Thus, the time lags
indicate that the water level will have the same tidal phase after 1 hour.
The visualization of mean bathymetry at figure 5.5 is the main product of present
investigation at the period 1, hence for the period 2 and 3 at appendix VIII. The
bathymetry map shows three distinctive depth regions which are near the shore at the
South-East, the channel and the shallow area at the North-West. At the channel
which is the deeper part area, the water depths reach approximately 11 m. For the
shallow area at the both side, the results is limited to almost 4 m contour lines, due to
the limitation of DiSC which uses the dispersion relation as part of the linear wave
theory. The algorithm is out of reach at the shallow area due to the propagation of
waves is not linear. Therefore the dispersion relation near the shore is not valid.
The cross section is used to determine the morphodynamic changes (figure 5.5). In
this thesis, there are two ways to analyze the erosion or deposition over the cross
section area. Firstly, the water depth variation over the cross section (figure 5.6) after
subtracting with common references is identified. The shallower water depth is in
October and the deeper is in February. At the distance 150 m - 400 m the sediment
deposition due to the storm is obvious, the period 1 has different water depth
approximately 0.5 m with period 2 and 3. The effect of the storm on the berm (100 m
from A) was the transportation of it closer to the coast. This phenomenon is unusual
as we expect the long waves to immigrate the berm to the deeper area. The
comparison between three periods shows the deposition of sediment almost every
where, but the sediment source cannot be defined. Probably, the deposition is caused
by longshore sediment transport. Secondly, the slope variations over the cross section
(figure 5.7) show very interesting results. In the area with depth higher than 8 m, the
geomorphological features present common behavior. At the period 2, the effect of
the storm on the sediment features is obvious, whereas at the period 1 and 3 have the
similar slope at the water depth higher than 8 m and could be assumed the stable
condition of the system. The near shore which is the South-East area at the distance
81.81 m was changed significantly at the three periods. The comparison between
period 1 and period 2 is shown the deposition at that point. The slope at the period 1
is approximately 0.41º and become 0.07º at period 2 after 8 days. The changes slope
54
Coastal Geosciences and Engineering, University of Kiel
6. Discussion
after 8 days is indicated that the sediment almost deposits in everywhere but the most
significant at the shallow water area which have water depth around 4m-7m. After 8
months (comparison between period 2 and period 3) the slope at the distance 81.81m
becomes steeper 10 times than before (from 0.07º become 0.7º). The changes slope is
indicated the erosion along the cross section and the significant results is shown at
the near shore area (South-East). The storm brought the sea bottom topography to
conservative condition for the summer period.
SENET et al. (2001, 2004) identified the changes bathymetry between 2001 and
2003 for an area of the island of Sylt using ground based radar (figure 6.1). Close to
the shore loss sand is obvious, whereas a broad stripe between 200 m and 800 m
distance from shore shows a significant increase of sand and at the distance around
1000 m is the sand reduction zone. These results have been verified by conventional
observation.
Coastal Geosciences and Engineering, University of Kiel
55
6. Discussion
56
Coastal Geosciences and Engineering, University of Kiel
7. Conclusion
7. Conclusion
The Dispersive Surface Classificator (DiSC) as remote sensing method for
interpreting of radar image sequences has been proven to be a powerful tool for
coastal remote sensing. The comprehensive DiSC method permits the determination
of spatial maps of important hydrographic parameter and the water depth. The
technique is particularly useful for monitoring the consequences of a severe storm
period, when the other monitoring systems are unusable.
In this thesis the potential of the DiSC algorithm has been examined to extract the
additional information on the momentary water level. The accuracy of the chosen
method was assessed with the chi-squared distribution to construct the confidence
interval of variance. It could be shown that by inversion of the local wave in space
and time, the in-situ gauge can be simulated. It is proven that the water level deduced
by the radar measurements is not diverging significantly from the tidal gauge. The
meteorological conditions, regional and local are important for the accuracy of the
method. In addition, the selection area with 81 neighboring cells, as occurred from
the method itself, is increasing the significance of the resulted water level. The
comparison between DiSC and tidal gauge water level has a significant correlation
(Corr=0.77). So, due to the capability of X-band radar to measure water depth, the
in-situ measurement in the nearshore area at the two positions in direct vicinity and
the closest gauge data can be used, when the time shift of the tidal phase is known.
The morphodynamic changes is also examined, by studying new bathymetry layer
along two cross sections at the ship channel in the List Tief. The characteristic of the
channel is changing (slope, absolute depth, and width).The slopes along two cross
sections are compared during three different periods and it shows the
deposition/erosion. The variability of sediment over the cross section is influenced
by extreme events (storm) as well as by seasonal phenomena. The long term March
to October has proved that in the area of investigation morphodynamic changes also
occur during the summer season.
The nautical X-band radar measurement as a remote sensing method for water depth
measurement in the coastal area has proven to get reasonable results in the severe
Coastal Geosciences and Engineering, University of Kiel
57
7. Conclusion
weather condition. The advantage of using an X-band radar system is its ability to
monitor the coastal processes remotely and continuously, under calm condition as
well as stormy. Hence, the X-band radar is satisfactory to observe the phenomena at
the coastal region.
.
58
Coastal Geosciences and Engineering, University of Kiel
References
References
AHRENDT, K. (2001): Expected effect of climate change on Sylt island: results
from a multidisciplinary German project. Clim. Res., 18: 141-146.
ANONYMOUS (1989): FURUNO – Operators manuals for FR 1201; Nishimomiya,
Japan (FURUNO ELECTRIC CO. LIMITED).
BARRICK, D. E. (1977): Ocean surface current mapped by Radar. Science 198: 138144.
BELL, P.S. (1999): Shallow water bathymetry derived from an analysis of X-band
marine radar images of waves. Coastal Engineering 37: 513-527.
BELL, P.S. (1998): Bathymetry derived from an analysis of X-band radar marine
radar images of waves. Proceeding of oceanology’98 conference, Bringhton,
England, vol.3. 535-543.
CHERRY, J.A. (1994): Distortion analysis of weakly nonlinear filters using volterra
series. Master’s thesis, Ottowa Carleton Institute for Electrical ngineering, Ottawa,
Canada.
CHOWDHURY, M.Z.R. (2007): Assessment of water flow and the impact on
sediment motion in a tidal channel of North Sylt basing on radar observation. Master
thesis, Coastal Geosciences and Engineering, CORELAB, University of Kiel,
Germany.
CROMBIE, D. D. (1956): Doppler spectrum of sea echo at 13.56 Mc/s. Nature, 175:
681-682.
DAVIS, J.C. (2002): Statistics and data analysis in geology (third edition). 638pp.;
New York, London, Toronto, Singapore (John willey & Sons).
Coastal Geosciences and Engineering, University of Kiel
59
References
DANKERT, H. & ROSENTHAL, W. (2004): Ocean surface determination from XBand radarimage sequences. Journal of Geophysical Research, 109, pp C04016.
DANKERT, H. (2004): Measurement of wave, wave groups, and wind fields using
nautical radar-image sequences. Dissertation, University of Hamburg, Germany.
DOONG, D. J. (2003): Uncertainty assessment of wave remote sensing, PhD thesis,
Department of Hydraulic and Ocean Engineering, National Cheng Kung University,
Tainan, Taiwan, Republic of China.
EMERY, W.J & THOMSON, E.R. (2001): Data analysis methods in physical
oceanography (second and revised edition). 638pp.; Amsterdam, London, New York,
Oxford, Paris, Tokyo (Elsivier).
FLAMPOURIS, S. (2006): Investigation of correlations between radar deduced
bathymetries due to the outer impact of a storm in the area “Salzsand”. Master thesis,
Coastal Geosciences and Engineering, CORELAB, University of Kiel, Germany.
GANGESKAR, R. & GRONLIE, O. (2000): Wave Height Measurement with a
Standard Navigation Ship Radar – Result from Field Trials. In: Proceedings of the
Sixth International Conference on Remote Sensing for Marine and Coastal
Environments, Charleston, South Carolina.
GRONLIE, O. (1995): Microwave Radar Directional Wave Measurements – MIROS
Results. In: Proceedings of the WMO/IOC Workshop on Operational Ocean
Monitoring using Surface Based Radars, WMO Report no. 32, WMO/TD-No. 694,
Geneva.
HASSELMANN, K. (1962): On the non-linear energy transfer in a gravity wave
spectrum. 1: General theory. J. Fluid Mech., 12, 481–500.
60
Coastal Geosciences and Engineering, University of Kiel
References
JAHID HASAN, G.M. & TAKEWAKA, S. (2007). Observation of a stormy wave
field with X-band radar and its linear aspect. Department of Engineering Mechanics
and Energy, University of Tsukuba, Tsukuba, Ibaraki, Japan.
JENSKINS, G. M. & WATTS, D.G. (1968): Spectral Analysis and Its Applications.
525pp.; San Francisco, Düsseldorf, Johannesburg, London, Panama, Singapore,
Sydney, Toronto (Holden-Day).
JOHN, W. (2002). Chi-Square Calculator, Mathematic Detail and Table.
(http://www.fourmilab.ch/rpkp/experiments/analysis/chiCalc.html).
LONG, M. W. (1983): Radar Reflectivity of Land and Sea (Second Edition). 385pp.;
Dedham (Artech House, Inc).
MISRA, S. K. et al. (2002): An approach to determining nearshore bathymetry using
remotely sensed ocean surface dynamics. Journal Coastal Engineering, 47, 265293p.
NIETO BORGE, J. C.; REICHERT, K.; DITTMER, J. & ROSENTHAL, W. (1998):
WaMoS II: A wave and current monitoring system, Presented at the COAST 714
conference, Sept., Paris Proceedings.
NIETO BORGE, J.C. & SOARES, C. G. (2000): Analysis of directional wave fields
using X-band navigation radar. Coastal Engineering, 40, 375-391.
NIETO BORGE, J.C.; REICHERT, K. & DITTMER, J. (1999): Use of nautical radar
as wave monitoring instrument. Coastal Engineering, 37, 331-342.
PHILLIPS, O.M. (1966): Thy dynamics of the upper ocean (First Edition);
Cambridge University Press.
Coastal Geosciences and Engineering, University of Kiel
61
References
PIERSON, W. J. (1962): The directional spectrum of a wind-generated sea as
determined from data obtained by the Stereo Wave Observation Project. Coll. Eng.
NYU Meteorol. Pap. 2, No. 6.
PIERSON, W. J., NEUMANN, G. & JAMES, R. W. (1955): Practical methods for
observing and forecasting ocean waves by means of wave spectra and statistics. US
Navy Hydrographic Office Pub., 603.
REISE, K. (2004): Sea-Level Rise and the Future of Barrier Island in the North Sea;
in proceedings of SeaLevel Rise and Coastal Defence in the Southern North Sea,
Norfolk on 18 March 2004, 38-43p.
ROBINSON, I.S., WARD, N.P., GOMMENGINER, C.P, & TENORIOGONZALES M.A (2000): Coastal oceanography applications of digital image data
from marine radar. Journal of Atmospheric and Oceanic Technology, 17, pp. 721725.
SABINS, F. F. (1987): Remote Sensing, Principles and Interpretation (Second
Edition). W.H. Freeman, New York.
SEEMANN, J., ZIEMER, F. & SENET, C. M. (1997): A method for computing
calibrated ocean wave spectra from measurements with a nautical X-band radar.
Proc. Oceans ’97, Halifax, NS, Canada, MTS/IEEE, 1148–1154.
SEEMANN, J.; SENET, C.M.; WOLFF, U. & ZIEMER, F. (2000a): Nautical Xband radar Image Processing: Monitoring of Morphodynamic Processes in Coastal
Waters, Ocean 2000, Conference Proceedings, Rhode Island, USA.
SEEMANN, J.; SENET, C.M.; WOLFF, U.; HATTEN, H. & ZIEMER, F. (2000b):
Hydrographic Parameter Maps Retrieved from Nautical Radar Image Sequences of
inhomogeneous Water Surfaces. IGARSS”2000, Conference Proceedings, Volume
V, pp. 1898-1900, Honolulu, Hawaii.
62
Coastal Geosciences and Engineering, University of Kiel
References
SEEMANN, J.; SENET, C.M.; ZIEMER, F. (2000c): Local analysis of
inhomogeneous Sea surfaces in Coastal waters using Nautical Radar Image
Sequences, Mustererkennung 2000, Springer, Berlin, Informatik aktuell, pp. 179186.
SENET, C., SEEMANN, J. & ZIEMER, F. (2001). The near-surface current velocity
determined from image sequences of the sea surface. IEEE Trans. Geosci. Remote
Sens., 39, 492–505.
SENET, C.M. (2004): Dynamics of Dispersive Boundaries: The determination of
Spatial Hydrographic-Parameter Maps from Optical Sea-Surface Image Sequences.
PhD thesis, GKSS Research Center, University of Hamburg.
SENET, C.M. & SEEMANN, J. (1999): Old_Pol_2_Cartesian (Computer Program),
Internal Resource, Radar Hydrography (KOR), GKSS Research Center GmbH,
Geesthacht, Germany.
SENET, C.M. & SEEMANN, J. (2002): Studie II: “Validation”. Technical report,
GKSS Research Center GmbH, Geesthacht, Germany.
SENET, C.M.; SEEMANN, J. & ZIEMER, F. (2003): Determination of Bathymetric
and Current Maps by the Method DiSC Based on the Analysis of Nautical X-Band
Radar-Image Sequences of the Sea Surface, (Elsevier Science).
SISTERMANS, P. & NIEUWENHUIS, O. (2007): Isle of Sylt: Isles ScheslwigHolstein (Germany)-a Case Study of European Initiative for Sustainable Coastal
Erosion Management (Eurosion), Amersfoort, The Netherlands. 21p.
SKOLNIK, M. (1990): Radar Handbook (Second Edition). McGraw-Hill, Inc., New
York, St. Louis, London, Lisbon, Madrid, Mexico, Paris, Singapore, Sydney, Tokyo,
Toronto.
Coastal Geosciences and Engineering, University of Kiel
63
References
SORENSEN, R. M. (1997): Basic Coastal Engineering (Second Edition). 301p.
Kluwer Academic Publishers, Boston, Dordrecht, London.
SOULSBY, R.L. & HUMPHERY, J.D. (1990): Field observations of wave-current
interaction at the sea bed, in Water Wave Kinematics, [eds] A. Torum and O.T.
Gudmestad, pp. 413-428. Kluwer Academic Publishers, Dordrecht.
Trizna, D, B. (2001): Errors in bathymetric retrieval using linear dispersion in 3-D
FFT analysis og image. Transactions on Geoscience and remote sensing, vol. 39, No.
11.
WILLEYWOLFF, U.; SEEMANN, J.; SENET, C.M. & ZIEMER, F. (1999):
Analysis of Morphodynamical Processes with a Nautical X-Band Rader,
Mustererkennung ‘99, Springer, Berlin, Ch. Pages 372-380.
YOO, J. (2007): Nonlinear bathymetry inversion based on wave property estimation
from nearshore video imagery. PhD thesis, Civil and Environmental Engineering,
Georgia Institute of Technology, USA.
YOUNG, I., ROSENTHAL, W., & ZIEMER, F. (1985). A three dimensional
analysis of marine radar images for the determination of ocean wave directionality
and surface currents. J. Geophys. Res., 90,C1, 1049–1059.
ZIEMER, F. & DITTMER, J. (1994): A System to Monitor Ocean Wave Fields. In:
Proceedings of the OCEANS’94, October 13-16: 28-31.
ZIEMER, F. (1991): Directional spectra from shipboard navigation radar during
LEWEX. In Directional Ocean Wave Spectra, edited by R.C. Beal, The Johns
Hopkins University Press, Baltimore, USA, pp. 80-84.
64
Coastal Geosciences and Engineering, University of Kiel
References
ZIEMER, F. (1995): An Instrument for the Survey of the Directionality of the Ocean
Wave Field. Workshop on Operational Ocean Monitoring using surface based radars,
Geneva, WMO/IOC Report No. 32, pp. 81-87.
ZIEMER, F., BROCKMANN, C.; VAUGHAN, A. R.; SEEMANN, J. & SENET,
C.M. (2004): Radar Survey of Near Shore Bathymetry within the OROMA project.
EARSel eProceedings 3, 2/2004, pp. 282-288.
Coastal Geosciences and Engineering, University of Kiel
65
References
66
Coastal Geosciences and Engineering, University of Kiel
Appendices
I. Appendix
Figure I-1: Sand nourishment at Sylt (GENERALPLAN KUSTENSCHUTZ).
Coastal Geosciences and Engineering, University of Kiel
A1
Appendices
II. Appendix
4
20
wind
radar water level
18
3
16
2
1
wind (m /s)
12
0
10
8
-1
W ater Level (m )
14
6
-2
4
-3
2
0
-4
4:30
3:30
3:00
2:30
2:00
1:30
1:00
0:30
0:00
23:30
23:00
22:30
22:00
21:30
21:00
20:30
20:00
19:30
19:00
18:30
18:00
17:30
17:00
Time
Figure II-1: plot wind speed and water level at the period 1(27 February 2002).
4
20
Wind
18
radar water level
3
16
2
1
W ind (m /s)
12
10
0
8
-1
6
-2
4
-3
2
0
-4
A2
Coastal Geosciences and Engineering, University of Kiel
18:00
Figure II-2: Plot wind speed and water level at the period 2 (7 March 2002).
17:00
16:00
15:00
14:00
13:00
12:00
11:00
10:00
9:00
8:00
7:00
Time
W ater Level (m )
14
Appendices
4
20
wind
radar water level
18
3
16
2
1
W ind (m /s)
12
10
0
8
-1
W ater Level (m )
14
6
-2
4
-3
2
0
-4
16:00
15:00
14:00
13:00
12:00
11:00
10:00
9:00
8:00
7:00
6:00
5:00
Time
Figure II-3: Plot wind speed and water level at the period 3 (28 October 2002).
Coastal Geosciences and Engineering, University of Kiel
A3
Appendices
III. Appendix
330
4
wind dir
radar water level
320
3
310
2
1
290
280
0
270
-1
W ater level (m )
W ind Direction (degree)
300
260
-2
250
-3
240
230
-4
4:30
3:30
3:00
2:30
2:00
1:30
1:00
0:30
0:00
23:30
23:00
22:30
22:00
21:30
21:00
20:30
20:00
19:30
19:00
18:30
18:00
17:30
17:00
Time
Figure III-1: Plot wind direction and water level at the period 1 (26-27 February 2002).
330
4
wind dir
radar water level
320
3
310
2
1
290
280
0
270
-1
260
-2
250
-3
240
230
-4
Figure III-2: Plot wind direction and water level at the period 2 (7 March 2002).
A4
Coastal Geosciences and Engineering, University of Kiel
18:00
17:00
16:00
15:00
14:00
13:00
12:00
11:00
10:00
9:00
8:00
7:00
Time
W ater Level (m )
W ind Direction (degree)
300
Appendices
4
330
Wind dir
radar water level
320
3
310
2
1
290
0
280
270
-1
W ater Level (m )
W ind Direction (degree)
300
260
-2
250
-3
240
-4
230
16:00
15:00
14:00
13:00
12:00
11:00
10:00
9:00
8:00
7:00
6:00
5:00
Time (UTC)
Figure III-2: Plot wind speed and water level at the period 3 (28 October 2002).
Coastal Geosciences and Engineering, University of Kiel
A5
Appendices
IV. Appendix
;*******************************************************************************
; PV WAVE Header
;------------------------------------------------------------------------------; File name
:
start
; Residency
:
; Programe name :
After_DiSC_Processing
; Module name :
Bathymetry
; Version nr
:
1.0
; Date
:
05.11.2005
; Place
:
GKSS / Geesthacht
; Author
:
Stelios F.
; Email
:
stylianos.flampouris@gkss.de
;------------------------------------------------------------------------------; Descriptions
: Initializing the compiling of all the routines
;------------------------------------------------------------------------------;
;*******************************************************************************
RETALL
.LOCALS
DELVAR, /ALL
CLOSE, /ALL
DEVICE, /CLOSE
set_plot,'win32'
@stat_startup
@math_startup
;@sigpro_startup
;@ip_startup
.run E:\pv-wave\pro\coordinates
.run E:\pv-wave\pro\datarr_creation
.run E:\pv-wave\pro\filenamed
.run E:\pv-wave\pro\comparison
.run E:\pv-wave\pro\output
surfer_main
A6
Coastal Geosciences and Engineering, University of Kiel
Appendices
;*******************************************************************************
; PV WAVE Header
;------------------------------------------------------------------------------; File name
:
surfer_main
; Residency
:
; Programe name :
After_DiSC_Processing
; Module name :
Bathymetry
; Version nr
:
1.1
; Date
:
05.11.2005
; Place
:
GKSS / Geesthacht
; Author
:
Stelios F.
; Email
:
stylianos.flampouris@gkss.de
;------------------------------------------------------------------------------; Descriptions
: The main of the After_DiSC_Processing
;------------------------------------------------------------------------------;
;*******************************************************************************
PRO surfer_main
Print, '-------------------------------------Print, 'The surfer_main is running'
Print, 'By stelios f.
Print, 'GKSS Research Center
Print, '-------------------------------------WAIT,1
;The subroutine 'coordinates' reads the coordinates of the result
;from DiSC. The coordinates are in meters
coordinates, linenr
;The subroutine 'datarr_creation' reads the data and creates an array
datarr_creation, data_arr, linenr
; The subroutine 'filenamed' checks for the existence of the input
; data file and calls two more subroutines the 'comparison' and the
; 'output'
filenamed, lookfor, data_arr
END
Coastal Geosciences and Engineering, University of Kiel
A7
Appendices
;*******************************************************************************
; PV WAVE Header
;------------------------------------------------------------------------------; File name
:
coordinates
; Residency
:
; Programe name :
After_DiSC_Processing
; Module name :
Bathymetry
; Version no
:
1.1
; Date
:
05.11.2005
; Place
:
GKSS / Geesthacht
; Author
:
Stelios F.
; Email
:
stylianos.flampouris@gkss.de
;------------------------------------------------------------------------------; Description
: The subroutine 'coordinates' is reading the coordinates of the resuls from DiSC.
The coordinates are in meters
;------------------------------------------------------------------------------;
;*******************************************************************************
PRO coordinates, linenr
Print, '-------------------------------------Print, 'The coordinates is running'
Print, '--------------------------------------
OPENW,1,'coordinates.txt'
FOR xcoordinate = DOUBLE(3460208),
DOUBLE(3462171.636),DOUBLE(40.9092) DO BEGIN
FOR ycoordinate = DOUBLE(6102504.6),
DOUBLE(6104468.236),DOUBLE(40.9092) DO BEGIN
xcoordinate1 = STRING(xcoordinate - 0.0208,format="(D12.2)")
;Print, 'xcoordinate1= ', xcoordinate1
ycoordinate1 = STRING(ycoordinate - 0.0208,format="(D12.2)")
;Print, 'ycoordinate1= ', ycoordinate1
coordinates = xcoordinate1+' '+ ycoordinate1
PRINTF,1, coordinates
ENDFOR ;ycoordinate
ENDFOR ;xcoordinate
CLOSE,1
;Counting the lines
linenr = LONG(0)
OPENR,1, 'coordinates.txt'
WHILE (NOT EOF(1)) DO BEGIN
READF,1,line
linenr = linenr+1
ENDWHILE
;print, linenr
CLOSE,1
END
A8
Coastal Geosciences and Engineering, University of Kiel
Appendices
*******************************************************************************
; PV WAVE Header
;------------------------------------------------------------------------------; File name
:
datarr_creation
; Residency
:
; Programe name :
After_DiSC_Processing
; Module name :
Bathymetry
; Version no
:
1.0
; Date
:
05.11.2005
; Place
:
GKSS / Geesthacht
; Author
:
Stelios F.
; Email
:
stylianos.flampouris@gkss.de
;------------------------------------------------------------------------------; Descriptions
:
The datarr_creation reads the data and creates an array
;------------------------------------------------------------------------------;
;*******************************************************************************
PRO datarr_creation, data_arr, linenr
Print, '-------------------------------------Print, 'The datarr_creation is running'
Print, '-------------------------------------;Creation of data array
data_arr=DBLARR(linenr,linenr)
lincnt = 0l
line = STRARR(1)
OPENU, 1, 'E:\pv-wave\main\coordinates.txt'
WHILE (NOT EOF(1)) DO BEGIN
READF,1,line
; To define the x_coordinate, have to find the position of the
;first point ".", so search for it
pos_firstpoint = STRPOS(line,'.')
x_coordinate = DOUBLE(STRMID(line,pos_firstpoint(0)-7,10))
data_arr(0,lincnt) = x_coordinate
;print,'x = ',x_coordinate
; To define the x_coordinate, have to find the position of the
;second point ".", so search for it
pos_secondpoint =STRPOS(line,'.',pos_firstpoint(0)+1)
;print,'pos_secondpoint=',pos_secondpoint
y_coordinate = DOUBLE(STRMID(line,pos_secondpoint(0)-7,pos_secondpoint(0)pos_firstpoint(0)-1))
data_arr(1,lincnt) = y_coordinate
;print,'y_coordinate=',data_arr(1,lincnt)
lincnt = lincnt+1
ENDWHILE
CLOSE,1
END
Coastal Geosciences and Engineering, University of Kiel
A9
Appendices
;*******************************************************************************
; PV WAVE Header
;------------------------------------------------------------------------------; File name
:
filenamed
; Residency
:
; Programe name :
After_DiSC_Processing
; Module name :
Bathymetry
; Version no
:
1.0
; Date
:
05.11.2005
; Place
:
GKSS / Geesthacht
; Author
:
Stelios F.
; Email
:
stylianos.flampouris@gkss.de
;------------------------------------------------------------------------------; Descriptions
:
The subroutine 'filenamed' checks for the existence of the input data file
and calls two more subroutines the ‘comparison’ and the ‘output’
;
;------------------------------------------------------------------------------;
;*******************************************************************************
PRO filenamed, lookfor, data_arr
Print, '-------------------------------------Print, 'The filenamed is running'
Print, '-------------------------------------fn=LONG(2)
existfiles_strvec = STRARR(1)
;definition of the variables
FOR day = 28, 29, 1 DO BEGIN
FOR hour = 0, 23, 1 DO BEGIN
FOR shoot = 1,4, 1 DO BEGIN
day1 = STRCOMPRESS(STRING(day),/Remove_all)
daylen = STRLEN(day1)
IF daylen LT 2 THEN BEGIN
day1 = '0'+ day1
ENDIF ELSE BEGIN
day1 = day1
ENDELSE
hour1 = STRCOMPRESS(STRING(hour),/Remove_all)
hourlen = STRLEN(hour1)
IF hourlen LT 2 THEN BEGIN
hour1 = '0'+hour1
ENDIF ELSE BEGIN
hour1 = hour1
ENDELSE
shoot1 = STRCOMPRESS (STRING(shoot),/Remove_all)
shootlen = STRLEN (shoot1)
IF shootlen LT 2 THEN BEGIN
shoot1 = '0'+shoot1
ENDIF ELSE BEGIN
shoot1 = shoot1
ENDELSE
A10
Coastal Geosciences and Engineering, University of Kiel
Appendices
fname = '10'+day1+hour1+'00_'+shoot1+'_result_6x6.txt'
;Existence of file
f_path = 'E:/2002_re/Oct/1028/'
lookfor = f_path+fname
;print, 'lookfor=', lookfor
file_exist=FINDFILE(lookfor, count = fe_counter)
IF fe_counter EQ 1 THEN BEGIN
existfiles_strvec = [existfiles_strvec,file_exist]
;PRINT, lookfor
;PRINT,existfiles_strvec
;HAK
comparison, lookfor, data_arr, fn
fn=fn+1
ENDIF
ENDFOR ;shoot
ENDFOR ;hour
ENDFOR ;day
output, data_arr
END
Coastal Geosciences and Engineering, University of Kiel
A11
Appendices
;*******************************************************************************
; PV WAVE Header
;------------------------------------------------------------------------------; File name
:
coordinates
; Residency
:
; Programe name :
After_DiSC_Processing
; Module name :
Bathymetry
; Version no
:
1.1
; Date
:
05.11.2005
; Place
:
GKSS / Geesthacht
; Author
:
Stelios F.
; Email
:
stylianos.flampouris@gkss.de
;------------------------------------------------------------------------------; Descriptions
:
The subroutine 'comparison' creates an index which matches the
'coordinates' with the coordinates of the result from DiSC and simultunuously the results are filtered
but the number of regression points (GT 40)
;------------------------------------------------------------------------------;
;*******************************************************************************
PRO comparison, lookfor, data_arr, fn
Print, '-------------------------------------Print, 'The comparison number
Print, fn
Print, '-------------------------------------;Creation of the full data array with the correct coordinates..!
lincnt = 0l
line = STRARR(1)
OPENR, 1, lookfor
WHILE (NOT EOF(1)) DO BEGIN
READF,1,line
;print, line
; To define the x_coordinate of the data, have to find the position of the
;first point ".", so search for it
pos_firstpoint = STRPOS(line,'.')
;print,'pos_firstpoint = ',pos_firstpoint
x_coordinate = DOUBLE(STRMID(line,pos_firstpoint(0)-7,10))
;print, 'x_coordinate=', x_coordinate
; To define the y_coordinate of the data, have to find the position of the
;second point ".", so search for it
pos_secondpoint = STRPOS(line,'.',pos_firstpoint(0)+1)
;print,'pos_secondpoint = ',pos_secondpoint
y_coordinate = DOUBLE(STRMID(line,pos_secondpoint(0)-7,pos_secondpoint(0)pos_firstpoint(0)-1))
;print, 'y_coordinate=', y_coordinate
;For qualifying reasons the regression points of each "depth" must be more than 40
;So first read the regression points anf if greater than 40,we accept the calculated depth
pos_secondtab = STRPOS(line,' ',pos_secondpoint(0)+1)
;pos_secondtab = STRPOS(line,' ',pos_secondpoint(0)+1)
;print,'pos_secondtab = ',pos_secondtab
nr_reg_point = DOUBLE(STRMID(line,pos_secondtab(0),4))
;print, 'nr_reg_point', nr_reg_point
A12
Coastal Geosciences and Engineering, University of Kiel
Appendices
;To define the depth, have to find the position of the third point "."
pos_thirdpoint = STRPOS(line,'.',pos_secondpoint(0)+1)
;print,'pos_thirdpoint = ',pos_thirdpoin
depth = DOUBLE(STRMID(line,pos_thirdpoint(0)-2,5))
;print,'depth =', depth
IF nr_reg_point(0) LT 40 OR (depth(0)LT 4 OR depth(0) GT 18) THEN BEGIN
depth=0
;print,'depth1 =', depth
ENDIF ELSE BEGIN
;Index
x_index = WHERE(
$
(data_arr(0,*) LE x_coordinate(0) + 10.0) AND $
(data_arr(0,*) GT x_coordinate(0) - 10.0) $
)
;PRINT,'x_index', x_index
if (x_index(0) EQ -1) then STOP
y_index = WHERE(
$
(data_arr(1,x_index) LE y_coordinate(0) + 10.0)
(data_arr(1,x_index) GT y_coordinate(0) - 10.0)
)
AND $
$
right_line = x_index(y_index)
;PRINT, right_line
data_arr(fn,right_line) = depth(0)
;PRINT,'Z=', data_arr(fn,right_line)
ENDELSE
lincnt = lincnt+1
ENDWHILE
CLOSE,1
END
Coastal Geosciences and Engineering, University of Kiel
A13
Appendices
;*******************************************************************************
; PV WAVE Header
;------------------------------------------------------------------------------; File name
:
coordinates
; Residency
:
; Programe name :
After_DiSC_Processing
; Module name :
Bathymetry
; Version nr
:
1.0
; Date
:
05.11.2005
; Place
:
GKSS / Geesthacht
; Author
:
Stelios F.
; Email
:
stylianos.flampouris@gkss.de
;------------------------------------------------------------------------------; Description
: The subroutine 'output' extracts the data into two different files.
The coordinates : coor_result.txt
; The data
: data_result.txt
;------------------------------------------------------------------------------;
;*******************************************************************************
PRO output, data_arr
Print, '-------------------------------------Print, 'The output is running'
Print, '-------------------------------------;Output subroutine
;Coordinates Output
OPENW,1, 'E:\pv-wave\main\coordinates.txt'
for j=0l,2302 do begin
str_dum1=''
for i=0l,2 do begin
str_line1 = STRING(data_arr(i,j), format="(D12.2)")
str_dum1=str_dum1 + str_line1
endfor ; column
PRINTF,1,str_dum1
endfor ; lines
CLOSE,1
;Data Output
OPENW,1, 'E:\pv-wave\main\data_result.txt'
for j=0l,2302 do begin
str_dum=''
for i=2,58 do begin
str_line = STRING(data_arr(i,j), format="(D6.2)")
str_dum=str_dum + str_line
endfor ; column
PRINTF,1,str_dum
endfor ; lines
CLOSE,1
END
A14
Coastal Geosciences and Engineering, University of Kiel
Appendices
;*******************************************************************************
; PV WAVE Header
;------------------------------------------------------------------------------; File name
:
cross_correlation
; Residency
:
; Programe name :
Cross_correlation_processing
; Module name :
Water level
; Version nr
:
1.1
; Date
:
03.01.2008
; Place
:
GKSS / Geesthacht
; Author
:
Novrizal Alamsyah
; Email
:
nalamsyah@gkss.de
;------------------------------------------------------------------------------; Description
:
Initializing the compiling of all routines
;------------------------------------------------------------------------------;
;*******************************************************************************
Retall
.Locals
Delvar, /ALL
Close, /ALL
Device, /Close
set_plot,'win32'
@stat_startup
@math_startup
@sigpro_startup
@ip_startup
.run ../sub/baca_1
.run ../sub/cross_correlation
.run mulai_main
mulai_main
Coastal Geosciences and Engineering, University of Kiel
A15
Appendices
;********************************************************************************
;
;------------------------------------------------------------------------------; Description
:
The main of the Cross_correlation_processing
;------------------------------------------------------------------------------;
;********************************************************************************
;first step with pv-wave
PRO mulai_main
baca_1,time,Westerland_waterlevel,List_waterlevel,linenr2
cross_correlation,westerland_waterlevel,list_waterlevel,linenr2
END
A16
Coastal Geosciences and Engineering, University of Kiel
Appendices
;*******************************************************************************
;
;------------------------------------------------------------------------------; Description
:
The Subroutine 'baca_1' is reading the water level data
;------------------------------------------------------------------------------;
;*******************************************************************************
PRO baca_1,time,Westerland_waterlevel,List_waterlevel,linenr2
path1 ='E:/cross_correlation_data/102802_3.txt'
line =STRARR(1)
linenr =LONG(0)
linenr2 =LONG(0)
OPENER,1,path1
WHILE (NOT EOF(1)) DO BEGIN
READF,1,line
linenr = linenr+1
ENDWHILE
CLOSE,1
time
=STRARR(linenr+1)
Westerland_waterlevel =STRARR(linenr+1)
List_waterlevel
=STRARR(linenr+1)
OPENR,1,path1
WHILE (NOT EOF(1)) DO BEGIN
READF,1,line
time
(linenr2)
= STRMID(line,0,10)
Westerland_waterlevel (linenr2)
= STRMID(line,10,13)
List_waterlevel
(linenr2)
= STRMID(line,23,13)
linenr2
= linenr2+1
ENDWHILE
CLOSE, 1
;print, 'time= ', time
print, 'Westerland_waterlevel=', Westerland_waterlevel
print, 'List_waterlevel=',List_waterlevel
END
Coastal Geosciences and Engineering, University of Kiel
A17
Appendices
;*******************************************************************************
;
;------------------------------------------------------------------------------; Description
:
Comparison water level data
;------------------------------------------------------------------------------;
;*******************************************************************************
PRO cross_correlation,westerland_waterlevel,list_waterlevel,linenr2
linenr2=linenr2+1
cros_res = CROSSCORRELATION (linenr2, westerland_waterlevel,list_waterlevel, 6)
Print, cros_res
END
A18
Coastal Geosciences and Engineering, University of Kiel
Appendices
V. Appendix
Figure V-1: Plot of upper limit, lower limit (
ν
ν
) vs. ν
,
χν (α / 2) χν (1 − α / 2)
for
(1 − α ) =
0.80, 0.95, 0.99 (derived from JENKINS and WATTSS (1968), “Spectral Analysis and its
Application”).
Coastal Geosciences and Engineering, University of Kiel
A19
Appendices
Figure V-2: Table of Chi-Squared (derived from Newbold (1984), “Statistics for Business and
Economics”).
A20
Coastal Geosciences and Engineering, University of Kiel
Appendices
VI. Appendix
a.
4
3
2
Water Level (m)
1
0
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
12:00
13:00
14:00
15:00
16:00
-1
radar
-2
gauge
-3
-4
Time (UTC)
b.
4
3
Water Level (m)
2
1
0
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
-1
-2
radar
gauge
-3
-4
Time (UTC)
Figure VI-1: Graph representing the tidal cycle during period 3 at 28 October 2002 after
subtracting the mean water level of the series from every time step. The pink line is tidal gauge
measurement in Westerland and the blue line is the estimated tidal cycle from radar sequences.
The bars show confidence interval of variance. a. the average radar water level at the 81
neighboring cells around the point (3460944.34, 6103240.84); b. the average radar water level
after filtering with ± 0.25 m at the 81 neighboring cells.
Coastal Geosciences and Engineering, University of Kiel
A21
Appendices
VII. Appendix
Figure VII-2: Atmospheric pressure (barometric phenomena) (FLAMPOURIS 2008), Sylt is
denoted with black arrow.
A22
Coastal Geosciences and Engineering, University of Kiel
Appendices
VIII. Appendix
Figure VIII-1: Depth of the area of investigation during the storm period 2 (7 March 2002), as a
result of averaging the calculated depths for 12 hours. The R symbol is the radar position. The
white dot is the cross section A-B and C-D.
Coastal Geosciences and Engineering, University of Kiel
A23
Appendices
Figure VIII-2: Depth of the area of investigation during the storm period 3 (28 October 2002),
as a result of averaging the calculated depths for 12 hours. The R symbol is the radar position.
The white dot is the cross section A-B and C-D.
A24
Coastal Geosciences and Engineering, University of Kiel
Appendices
IX. Appendix
7th March 2002, 07:00
7th March 2002, 08:00
Coastal Geosciences and Engineering, University of Kiel
A25
Appendices
7th March 2002, 09:00
7th March 2002, 10:00
A26
Coastal Geosciences and Engineering, University of Kiel
Appendices
7th March 2002, 11:00
7th March 2002, 12:00
Coastal Geosciences and Engineering, University of Kiel
A27
Appendices
7th March 2002, 13:00
7th March 2002, 14:00
A28
Coastal Geosciences and Engineering, University of Kiel
Appendices
7th March 2002, 15:00
7th March 2002, 16:00
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Appendices
7th March 2002, 17:00
7th March 2002, 18:00
Figure IX-1: Visualization of hourly bathymetries of one tidal cycle, during period 2 (7th March
2002).
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Coastal Geosciences and Engineering, University of Kiel
Appendices
IX. Appendix
7th March 2002, 07:00
7th March 2002, 08:00
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Appendices
7th March 2002, 09:00
7th March 2002, 10:00
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Appendices
7th March 2002, 11:00
7th March 2002, 12:00
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Appendices
7th March 2002, 13:00
7th March 2002, 14:00
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Appendices
7th March 2002, 15:00
7th March 2002, 16:00
Coastal Geosciences and Engineering, University of Kiel
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Appendices
7th March 2002, 17:00
7th March 2002, 18:00
Figure IX-1: Visualization of hourly bathymetries of one tidal cycle, during period 2 (7th March
2002).
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Coastal Geosciences and Engineering, University of Kiel
Appendices
X. Appendix
0
-0.5
feb/27/02-feb/28/02
march/07/02
oct/28/02
-1
-1.5
-2
Depth (m)
-2.5
-3
-3.5
-4
-4.5
-5
-5.5
-6
-6.5
-7
0
25
50
75
100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
Distance (m)
Figure X-1: The comparison of depth at the cross section C-D during the three difference
periods; the reference is defined as the average of water level in 2002 (see figure 5.6).
1
feb/26/02-feb/27/02
march/07/02
0.9
oct/28/02
0.8
Slope (degree)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
25
50
75
100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
Distance (m)
Figure X-2: The comparison of the slope over the cross section (C to D) for the three different
periods (see figure 5.6).
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